[{"title":"Universality in low-dimensional BCS theory","_id":"14542","issue":"9","year":"2024","oa_version":"Published Version","month":"10","article_processing_charge":"Yes (in subscription journal)","OA_type":"hybrid","arxiv":1,"ddc":["510"],"acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","abstract":[{"lang":"eng","text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."}],"date_published":"2024-10-01T00:00:00Z","scopus_import":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"file":[{"success":1,"checksum":"2b053a4223b4db14b90520999ec56054","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","date_updated":"2025-01-09T07:56:28Z","content_type":"application/pdf","creator":"dernst","date_created":"2025-01-09T07:56:28Z","access_level":"open_access","file_id":"18786","file_size":503910,"relation":"main_file"}],"oa":1,"article_type":"original","publication_status":"published","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"},{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","orcid":"0000-0003-4476-2288"},{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","first_name":"Barbara","last_name":"Roos","orcid":"0000-0002-9071-5880"}],"day":"01","publisher":"World Scientific Publishing","doi":"10.1142/s0129055x2360005x","type":"journal_article","ec_funded":1,"related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"},{"status":"public","relation":"dissertation_contains","id":"18135"}]},"citation":{"short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9. World Scientific Publishing, 2024.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>.","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2024). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2024;36(9). doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>."},"volume":36,"publication":"Reviews in Mathematical Physics","OA_place":"publisher","has_accepted_license":"1","date_updated":"2026-04-07T13:01:40Z","corr_author":"1","external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        36","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"date_created":"2023-11-15T23:48:14Z","file_date_updated":"2025-01-09T07:56:28Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"article_number":"2360005 "},{"article_processing_charge":"Yes","month":"09","oa_version":"Published Version","year":"2024","_id":"18107","title":"Pressure of a dilute spin-polarized Fermi gas: Lower bound","author":[{"last_name":"Lauritsen","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert"}],"project":[{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"publication_status":"published","article_type":"original","oa":1,"file":[{"date_updated":"2024-09-23T09:56:17Z","file_name":"2024_ForumMath_Lauritsen.pdf","success":1,"checksum":"330b881240013213a8e08538fec13d29","file_id":"18126","file_size":599886,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_created":"2024-09-23T09:56:17Z"}],"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","scopus_import":"1","abstract":[{"lang":"eng","text":"We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions  d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order  adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and  ρ  is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260)."}],"date_published":"2024-09-09T00:00:00Z","acknowledgement":"Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged.","arxiv":1,"ddc":["510"],"publication":"Forum of Mathematics, Sigma","volume":12,"citation":{"chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>.","ama":"Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. 2024;12. doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>","ieee":"A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 12. Cambridge University Press, 2024.","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 12, e78, Cambridge University Press, 2024, doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>.","ista":"Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78.","short":"A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024)."},"related_material":{"record":[{"id":"18135","relation":"dissertation_contains","status":"public"}]},"type":"journal_article","day":"09","doi":"10.1017/fms.2024.56","publisher":"Cambridge University Press","article_number":"e78","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"date_created":"2024-09-20T12:25:25Z","file_date_updated":"2024-09-23T09:56:17Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_identifier":{"issn":["2050-5094"]},"intvolume":"        12","language":[{"iso":"eng"}],"quality_controlled":"1","external_id":{"isi":["001307817400001"],"arxiv":["2407.05990"]},"corr_author":"1","date_updated":"2026-04-07T13:01:40Z","has_accepted_license":"1"},{"file_date_updated":"2024-09-26T13:12:55Z","date_created":"2024-09-24T10:56:25Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-042-8"]},"date_updated":"2026-04-16T08:17:55Z","has_accepted_license":"1","OA_place":"publisher","supervisor":[{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"corr_author":"1","citation":{"ieee":"A. B. Lauritsen, “Energies of dilute Fermi gases and universalities in BCS theory,” Institute of Science and Technology Austria, 2024.","ista":"Lauritsen AB. 2024. Energies of dilute Fermi gases and universalities in BCS theory. Institute of Science and Technology Austria.","mla":"Lauritsen, Asbjørn Bækgaard. <i>Energies of Dilute Fermi Gases and Universalities in BCS Theory</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18135\">10.15479/at:ista:18135</a>.","apa":"Lauritsen, A. B. (2024). <i>Energies of dilute Fermi gases and universalities in BCS theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18135\">https://doi.org/10.15479/at:ista:18135</a>","short":"A.B. Lauritsen, Energies of Dilute Fermi Gases and Universalities in BCS Theory, Institute of Science and Technology Austria, 2024.","chicago":"Lauritsen, Asbjørn Bækgaard. “Energies of Dilute Fermi Gases and Universalities in BCS Theory.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18135\">https://doi.org/10.15479/at:ista:18135</a>.","ama":"Lauritsen AB. Energies of dilute Fermi gases and universalities in BCS theory. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18135\">10.15479/at:ista:18135</a>"},"page":"353","publisher":"Institute of Science and Technology Austria","doi":"10.15479/at:ista:18135","day":"23","related_material":{"record":[{"relation":"part_of_dissertation","id":"11732","status":"public"},{"status":"public","id":"14542","relation":"part_of_dissertation"},{"id":"18107","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"17240"},{"status":"public","id":"14931","relation":"part_of_dissertation"}]},"type":"dissertation","ec_funded":1,"project":[{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"},{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"publication_status":"published","author":[{"first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","orcid":"0000-0003-4476-2288"}],"file":[{"success":1,"checksum":"c7bc3b31e430d57c65393051ca439575","file_name":"Lauritsen-thesis-final.pdf","date_updated":"2024-09-26T13:11:24Z","content_type":"application/pdf","date_created":"2024-09-26T13:11:24Z","creator":"alaurits","access_level":"open_access","file_id":"18147","file_size":3648831,"relation":"main_file"},{"date_updated":"2024-09-26T13:12:55Z","file_name":"Lauritsen-thesis-source.zip","checksum":"39f6b1b7f83e25a3bf9f933f1ea0bc06","file_size":1625888,"relation":"source_file","file_id":"18148","access_level":"closed","date_created":"2024-09-26T13:12:55Z","creator":"alaurits","content_type":"application/x-zip-compressed"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"abstract":[{"text":"This thesis consists of two separate parts. In the first part we consider a dilute Fermi gas interacting through a repulsive interaction in dimensions $d=1,2,3$. Our focus is mostly on the physically most relevant dimension $d=3$ \r\nand the setting of a spin-polarized (equivalently spinless) gas, where the Pauli exclusion principle plays a key role. We show that, at zero temperature, the ground state energy density of the interacting spin-polarized gas differs (to leading order) from that of the free (i.e. non-interacting) gas by a term of order $a_p^d\\rho^{2+2/d}$  with $a_p$ the $p$-wave scattering length of the repulsive interaction and $\\rho$ the density. Further, we extend this to positive temperature and show that the pressure of an interacting spin-polarized gas differs from that of the free gas by a now temperature dependent term, again of order $a_p^d\\rho^{2+2/d}$. Lastly, we consider the setting of a spin-$\\frac{1}{2}$ Fermi gas in $d=3$ dimensions and show that here, as an upper bound, the ground state energy density differs from that of the free system by a term of order $a_s \\rho^2$ with an error smaller than $a_s \\rho^2 (a_s\\rho^{1/3})^{1-\\eps}$ for any $\\eps > 0$, where $a_s$ is the $s$-wave scattering length of the repulsive interaction. \r\n\r\nThese asymptotic formulas complement the similar formulas in the literature for the dilute Bose and spin-$\\frac{1}{2}$ Fermi gas, where the ground state energies or pressures differ from that of the corresponding free systems by a term of order $a_s \\rho^2$ in dimension $d=3$. In the spin-polarized setting, the corrections, of order $a_p^3\\rho^{8/3}$ in dimension $d=3$, are thus much smaller and requires a more delicate analysis.\r\n\r\nIn the second part of the thesis we consider the Bardeen--Cooper--Schrieffer (BCS) theory of superconductivity and in particular its associated critical temperature and energy gap. We prove that the ratio of the zero-temperature energy gap and critical temperature $\\Xi(T=0)/T_c$ approaches a universal constant $\\pi e^{-\\gamma}\\approx 1.76$ in both the limit of high density in dimension $d=3$ and in the limit of weak coupling in dimensions $d=1,2$. This complements the proofs in the literature of this universal behaviour in the limit of weak coupling or low density in dimension $d=3$. Secondly, we prove that the ratio of the energy gap at positive temperature and critical temperature $\\Xi(T)/T_c$ approaches a universal function of the relative temperature $T/T_c$ in the limit of weak coupling in dimensions $d=1,2,3$.","lang":"eng"}],"date_published":"2024-09-23T00:00:00Z","status":"public","ddc":["515","539"],"degree_awarded":"PhD","article_processing_charge":"No","alternative_title":["ISTA Thesis"],"month":"09","year":"2024","_id":"18135","oa_version":"Published Version","title":"Energies of dilute Fermi gases and universalities in BCS theory"},{"issue":"7","_id":"14931","year":"2024","oa_version":"Published Version","title":"Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion","article_processing_charge":"Yes (via OA deal)","month":"04","scopus_import":"1","abstract":[{"lang":"eng","text":"We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15]."}],"date_published":"2024-04-01T00:00:00Z","status":"public","arxiv":1,"ddc":["510"],"acknowledgement":"A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged.","publication_status":"published","article_type":"original","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"author":[{"orcid":"0000-0003-4476-2288","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","isi":1,"file":[{"checksum":"ee203cf2dc4420ad90d3c9970d246a78","success":1,"date_updated":"2024-07-22T11:11:56Z","file_name":"2024_JourFunctAnalysis_Lauritsen.pdf","access_level":"open_access","creator":"dernst","date_created":"2024-07-22T11:11:56Z","content_type":"application/pdf","relation":"main_file","file_size":1381063,"file_id":"17305"}],"oa":1,"citation":{"chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>.","ama":"Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. 2024;286(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>, vol. 286, no. 7, 110320, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>.","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>","ista":"Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320.","ieee":"A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” <i>Journal of Functional Analysis</i>, vol. 286, no. 7. Elsevier, 2024.","short":"A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024)."},"volume":286,"publisher":"Elsevier","day":"01","doi":"10.1016/j.jfa.2024.110320","ec_funded":1,"type":"journal_article","related_material":{"record":[{"relation":"dissertation_contains","id":"18135","status":"public"}]},"publication":"Journal of Functional Analysis","quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"       286","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"has_accepted_license":"1","date_updated":"2026-04-16T08:17:56Z","corr_author":"1","external_id":{"isi":["001170294000001"],"arxiv":["2301.04894"]},"date_created":"2024-02-04T23:00:53Z","file_date_updated":"2024-07-22T11:11:56Z","department":[{"_id":"RoSe"}],"article_number":"110320","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"}},{"date_created":"2023-01-15T23:00:52Z","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        24","publication_identifier":{"issn":["1424-0637"]},"date_updated":"2025-04-14T07:26:59Z","corr_author":"1","external_id":{"arxiv":["2205.15284"],"isi":["000910751800002"]},"publication":"Annales Henri Poincare","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2205.15284"}],"citation":{"ama":"Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. 2023;24:1505-1560. doi:<a href=\"https://doi.org/10.1007/s00023-022-01252-3\">10.1007/s00023-022-01252-3</a>","chicago":"Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01252-3\">https://doi.org/10.1007/s00023-022-01252-3</a>.","short":"C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560.","mla":"Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 1505–60, doi:<a href=\"https://doi.org/10.1007/s00023-022-01252-3\">10.1007/s00023-022-01252-3</a>.","apa":"Boccato, C., &#38; Seiringer, R. (2023). The Bose Gas in a box with Neumann boundary conditions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01252-3\">https://doi.org/10.1007/s00023-022-01252-3</a>","ista":"Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 24, 1505–1560.","ieee":"C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary conditions,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 1505–1560, 2023."},"volume":24,"publisher":"Springer Nature","doi":"10.1007/s00023-022-01252-3","day":"01","page":"1505-1560","type":"journal_article","ec_funded":1,"publication_status":"published","article_type":"original","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"author":[{"last_name":"Boccato","full_name":"Boccato, Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"oa":1,"scopus_import":"1","abstract":[{"lang":"eng","text":"We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit."}],"date_published":"2023-05-01T00:00:00Z","status":"public","arxiv":1,"acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged.","article_processing_charge":"No","month":"05","_id":"12183","year":"2023","oa_version":"Preprint","title":"The Bose Gas in a box with Neumann boundary conditions"},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"department":[{"_id":"RoSe"}],"article_number":"17","date_created":"2023-08-22T14:09:47Z","file_date_updated":"2023-08-23T10:59:15Z","corr_author":"1","external_id":{"arxiv":["2206.14708"],"isi":["001032992600001"]},"has_accepted_license":"1","date_updated":"2024-10-09T21:06:41Z","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        26","publication":"Mathematical Physics, Analysis and Geometry","type":"journal_article","publisher":"Springer Nature","doi":"10.1007/s11040-023-09460-x","day":"26","volume":26,"citation":{"chicago":"Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11040-023-09460-x\">https://doi.org/10.1007/s11040-023-09460-x</a>.","ama":"Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum relation for the polaron. <i>Mathematical Physics, Analysis and Geometry</i>. 2023;26(3). doi:<a href=\"https://doi.org/10.1007/s11040-023-09460-x\">10.1007/s11040-023-09460-x</a>","ieee":"J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the energy–momentum relation for the polaron,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 26, no. 3. Springer Nature, 2023.","mla":"Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 26, no. 3, 17, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s11040-023-09460-x\">10.1007/s11040-023-09460-x</a>.","ista":"Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3), 17.","apa":"Lampart, J., Mitrouskas, D. J., &#38; Mysliwy, K. (2023). On the global minimum of the energy–momentum relation for the polaron. <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11040-023-09460-x\">https://doi.org/10.1007/s11040-023-09460-x</a>","short":"J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and Geometry 26 (2023)."},"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"file":[{"file_id":"14225","relation":"main_file","file_size":317026,"content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_created":"2023-08-23T10:59:15Z","date_updated":"2023-08-23T10:59:15Z","file_name":"2023_MathPhysics_Lampart.pdf","success":1,"checksum":"f0941cc66cb3ed06a12ca4b7e356cfd6"}],"author":[{"full_name":"Lampart, Jonas","first_name":"Jonas","last_name":"Lampart"},{"full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes","last_name":"Mitrouskas"},{"full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof","last_name":"Mysliwy"}],"publication_status":"published","article_type":"original","arxiv":1,"ddc":["510"],"acknowledgement":"D.M. and K.M. thank Robert Seiringer for helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria). Financial support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016, ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon 2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.) is gratefully acknowledged.","status":"public","abstract":[{"lang":"eng","text":"For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling."}],"scopus_import":"1","date_published":"2023-07-26T00:00:00Z","month":"07","article_processing_charge":"Yes (via OA deal)","keyword":["Geometry and Topology","Mathematical Physics"],"title":"On the global minimum of the energy–momentum relation for the polaron","oa_version":"Published Version","_id":"14192","issue":"3","year":"2023"},{"abstract":[{"lang":"eng","text":"In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with a much simplified proof. As a corollary we obtain a simple proof of the original Lieb–Thirring inequality."}],"scopus_import":"1","date_published":"2023-11-15T00:00:00Z","status":"public","acknowledgement":"J.P.S. thanks the Institute of Science and Technology Austria for the hospitality and support during a visit where this work was done. J.P.S. was also partially supported by the VILLUM Centre of Excellence for the Mathematics of Quantum Theory (QMATH) (grant No. 10059).","arxiv":1,"ddc":["510"],"publication_status":"published","article_type":"original","author":[{"first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer"},{"full_name":"Solovej, Jan Philip","first_name":"Jan Philip","last_name":"Solovej"}],"file":[{"relation":"main_file","file_size":232934,"file_id":"14915","access_level":"open_access","creator":"dernst","date_created":"2024-01-30T14:15:16Z","content_type":"application/pdf","date_updated":"2024-01-30T14:15:16Z","file_name":"2023_JourFunctionalAnalysis_Seiringer.pdf","checksum":"28e424ad91be6219e9d321054ce3a412","success":1}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"year":"2023","_id":"14254","issue":"10","oa_version":"Published Version","title":"A simple approach to Lieb-Thirring type inequalities","article_processing_charge":"Yes (via OA deal)","month":"11","intvolume":"       285","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"date_updated":"2024-10-09T21:06:47Z","has_accepted_license":"1","external_id":{"isi":["001071552300001"],"arxiv":["2303.04504"]},"corr_author":"1","date_created":"2023-09-03T22:01:14Z","file_date_updated":"2024-01-30T14:15:16Z","article_number":"110129","department":[{"_id":"RoSe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"ama":"Seiringer R, Solovej JP. A simple approach to Lieb-Thirring type inequalities. <i>Journal of Functional Analysis</i>. 2023;285(10). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">10.1016/j.jfa.2023.110129</a>","chicago":"Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">https://doi.org/10.1016/j.jfa.2023.110129</a>.","short":"R. Seiringer, J.P. Solovej, Journal of Functional Analysis 285 (2023).","ieee":"R. Seiringer and J. P. Solovej, “A simple approach to Lieb-Thirring type inequalities,” <i>Journal of Functional Analysis</i>, vol. 285, no. 10. Elsevier, 2023.","ista":"Seiringer R, Solovej JP. 2023. A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. 285(10), 110129.","apa":"Seiringer, R., &#38; Solovej, J. P. (2023). A simple approach to Lieb-Thirring type inequalities. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">https://doi.org/10.1016/j.jfa.2023.110129</a>","mla":"Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” <i>Journal of Functional Analysis</i>, vol. 285, no. 10, 110129, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">10.1016/j.jfa.2023.110129</a>."},"volume":285,"day":"15","doi":"10.1016/j.jfa.2023.110129","publisher":"Elsevier","type":"journal_article","publication":"Journal of Functional Analysis"},{"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"intvolume":"       404","quality_controlled":"1","language":[{"iso":"eng"}],"external_id":{"isi":["001096217400007"],"arxiv":["2207.03156"]},"corr_author":"1","date_updated":"2025-09-09T13:12:02Z","has_accepted_license":"1","department":[{"_id":"RoSe"}],"file_date_updated":"2023-10-31T12:21:39Z","date_created":"2023-10-22T22:01:13Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"volume":404,"citation":{"ieee":"M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” <i>Communications in Mathematical Physics</i>, vol. 404. Springer Nature, pp. 287–337, 2023.","apa":"Brooks, M., &#38; Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>","mla":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>, vol. 404, Springer Nature, 2023, pp. 287–337, doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>.","ista":"Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337.","short":"M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337.","chicago":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>.","ama":"Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. 2023;404:287-337. doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>"},"type":"journal_article","ec_funded":1,"page":"287-337","day":"01","publisher":"Springer Nature","doi":"10.1007/s00220-023-04841-3","publication":"Communications in Mathematical Physics","status":"public","abstract":[{"text":"We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation.","lang":"eng"}],"scopus_import":"1","date_published":"2023-11-01T00:00:00Z","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","ddc":["510"],"arxiv":1,"author":[{"full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","first_name":"Morris","orcid":"0000-0002-6249-0928","last_name":"Brooks"},{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"publication_status":"published","article_type":"original","oa":1,"file":[{"file_size":832375,"relation":"main_file","file_id":"14477","date_created":"2023-10-31T12:21:39Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf","file_name":"2023_CommMathPhysics_Brooks.pdf","date_updated":"2023-10-31T12:21:39Z","checksum":"1ae49b39247cb6b40ff75997381581b8","success":1}],"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","year":"2023","_id":"14441","title":"The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy","article_processing_charge":"Yes (via OA deal)","month":"11"},{"article_type":"original","publication_status":"published","author":[{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert"}],"file":[{"relation":"main_file","file_size":201513,"file_id":"14677","access_level":"open_access","date_created":"2023-12-11T12:03:12Z","creator":"dernst","content_type":"application/pdf","date_updated":"2023-12-11T12:03:12Z","file_name":"2023_JST_Seiringer.pdf","checksum":"9ce96ca87d56ea9a70d2eb9a32839f8d","success":1}],"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"scopus_import":"1","date_published":"2023-11-25T00:00:00Z","abstract":[{"text":"We consider a class of polaron models, including the Fröhlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential spectrum.","lang":"eng"}],"status":"public","OA_type":"diamond","ddc":["510"],"arxiv":1,"article_processing_charge":"Yes","month":"11","year":"2023","issue":"3","_id":"14662","oa_version":"Published Version","title":"Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling","date_created":"2023-12-10T23:00:59Z","file_date_updated":"2023-12-11T12:03:12Z","department":[{"_id":"RoSe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"intvolume":"        13","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1664-039X"],"eissn":["1664-0403"]},"date_updated":"2025-09-09T13:40:33Z","has_accepted_license":"1","OA_place":"publisher","external_id":{"arxiv":["2210.17123"],"isi":["001127467700008"]},"corr_author":"1","publication":"Journal of Spectral Theory","citation":{"mla":"Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling.” <i>Journal of Spectral Theory</i>, vol. 13, no. 3, EMS Press, 2023, pp. 1045–55, doi:<a href=\"https://doi.org/10.4171/JST/469\">10.4171/JST/469</a>.","ista":"Seiringer R. 2023. Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. 13(3), 1045–1055.","apa":"Seiringer, R. (2023). Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/469\">https://doi.org/10.4171/JST/469</a>","ieee":"R. Seiringer, “Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling,” <i>Journal of Spectral Theory</i>, vol. 13, no. 3. EMS Press, pp. 1045–1055, 2023.","short":"R. Seiringer, Journal of Spectral Theory 13 (2023) 1045–1055.","chicago":"Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling.” <i>Journal of Spectral Theory</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/JST/469\">https://doi.org/10.4171/JST/469</a>.","ama":"Seiringer R. Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. <i>Journal of Spectral Theory</i>. 2023;13(3):1045-1055. doi:<a href=\"https://doi.org/10.4171/JST/469\">10.4171/JST/469</a>"},"DOAJ_listed":"1","volume":13,"page":"1045-1055","day":"25","publisher":"EMS Press","doi":"10.4171/JST/469","type":"journal_article"},{"type":"journal_article","day":"01","doi":"10.1063/5.0172199","publisher":"AIP Publishing","volume":64,"citation":{"chicago":"Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number of Excitations in the Weakly Interacting Bose Gas.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2023. <a href=\"https://doi.org/10.1063/5.0172199\">https://doi.org/10.1063/5.0172199</a>.","ama":"Mitrouskas DJ, Pickl P. Exponential decay of the number of excitations in the weakly interacting Bose gas. <i>Journal of Mathematical Physics</i>. 2023;64(12). doi:<a href=\"https://doi.org/10.1063/5.0172199\">10.1063/5.0172199</a>","ieee":"D. J. Mitrouskas and P. Pickl, “Exponential decay of the number of excitations in the weakly interacting Bose gas,” <i>Journal of Mathematical Physics</i>, vol. 64, no. 12. AIP Publishing, 2023.","apa":"Mitrouskas, D. J., &#38; Pickl, P. (2023). Exponential decay of the number of excitations in the weakly interacting Bose gas. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0172199\">https://doi.org/10.1063/5.0172199</a>","ista":"Mitrouskas DJ, Pickl P. 2023. Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. 64(12), 121901.","mla":"Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number of Excitations in the Weakly Interacting Bose Gas.” <i>Journal of Mathematical Physics</i>, vol. 64, no. 12, 121901, AIP Publishing, 2023, doi:<a href=\"https://doi.org/10.1063/5.0172199\">10.1063/5.0172199</a>.","short":"D.J. Mitrouskas, P. Pickl, Journal of Mathematical Physics 64 (2023)."},"publication":"Journal of Mathematical Physics","external_id":{"arxiv":["2307.11062"],"isi":["001127432200002"]},"corr_author":"1","date_updated":"2025-09-09T14:05:28Z","has_accepted_license":"1","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"intvolume":"        64","language":[{"iso":"eng"}],"quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"121901","department":[{"_id":"RoSe"}],"file_date_updated":"2024-01-02T08:45:07Z","date_created":"2023-12-31T23:01:02Z","title":"Exponential decay of the number of excitations in the weakly interacting Bose gas","oa_version":"Published Version","year":"2023","issue":"12","_id":"14715","month":"12","article_processing_charge":"Yes (in subscription journal)","acknowledgement":"We thank Lea Boßmann, Phan Thành Nam and Simone Rademacher for helpful remarks. P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Grant No. SFB/TRR 352 “Mathematics of Many-Body Quantum Systems and Their Collective Phenomena.”","ddc":["510"],"arxiv":1,"status":"public","scopus_import":"1","date_published":"2023-12-01T00:00:00Z","abstract":[{"text":"We consider N trapped bosons in the mean-field limit with coupling constant λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation. We prove that the probability of finding ℓ particles outside the condensate wave function decays exponentially in ℓ.","lang":"eng"}],"oa":1,"file":[{"access_level":"open_access","creator":"dernst","date_created":"2024-01-02T08:45:07Z","content_type":"application/pdf","file_size":4346922,"relation":"main_file","file_id":"14722","checksum":"66572f718a36465576cf0d6b3f7e01fc","success":1,"date_updated":"2024-01-02T08:45:07Z","file_name":"2023_JourMathPhysics_Mitrouskas.pdf"}],"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","last_name":"Mitrouskas"},{"full_name":"Pickl, Peter","first_name":"Peter","last_name":"Pickl"}],"article_type":"original","publication_status":"published"},{"publication_status":"published","article_type":"original","author":[{"full_name":"Falconi, Marco","first_name":"Marco","last_name":"Falconi"},{"orcid":"0000-0002-0495-6822","last_name":"Leopold","full_name":"Leopold, Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K"},{"last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes"},{"orcid":"0000-0002-9166-5889","last_name":"Petrat","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","full_name":"Petrat, Sören P","first_name":"Sören P"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_published":"2023-01-09T00:00:00Z","abstract":[{"text":"We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively.","lang":"eng"}],"scopus_import":"1","status":"public","arxiv":1,"article_processing_charge":"No","month":"01","issue":"4","_id":"12430","year":"2023","oa_version":"Preprint","title":"Bogoliubov dynamics and higher-order corrections for the regularized Nelson model","date_created":"2023-01-29T23:00:59Z","department":[{"_id":"RoSe"}],"article_number":"2350006","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        35","publication_identifier":{"issn":["0129-055X"]},"date_updated":"2023-08-16T11:47:27Z","external_id":{"arxiv":["2110.00458"],"isi":["000909760300001"]},"publication":"Reviews in Mathematical Physics","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2110.00458"}],"citation":{"chicago":"Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/S0129055X2350006X\">https://doi.org/10.1142/S0129055X2350006X</a>.","ama":"Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>. 2023;35(4). doi:<a href=\"https://doi.org/10.1142/S0129055X2350006X\">10.1142/S0129055X2350006X</a>","ieee":"M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov dynamics and higher-order corrections for the regularized Nelson model,” <i>Reviews in Mathematical Physics</i>, vol. 35, no. 4. World Scientific Publishing, 2023.","apa":"Falconi, M., Leopold, N. K., Mitrouskas, D. J., &#38; Petrat, S. P. (2023). Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129055X2350006X\">https://doi.org/10.1142/S0129055X2350006X</a>","ista":"Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 35(4), 2350006.","mla":"Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>, vol. 35, no. 4, 2350006, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/S0129055X2350006X\">10.1142/S0129055X2350006X</a>.","short":"M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical Physics 35 (2023)."},"volume":35,"publisher":"World Scientific Publishing","day":"09","doi":"10.1142/S0129055X2350006X","type":"journal_article"},{"oa":1,"file":[{"access_level":"open_access","date_created":"2023-04-26T12:30:06Z","creator":"alaurits","content_type":"application/octet-stream","file_size":4567,"relation":"main_file","file_id":"12870","checksum":"85ede12d38bb8d944022a8cba4d719f5","success":1,"date_updated":"2023-04-26T12:30:06Z","file_name":"README.md"},{"file_id":"12871","file_size":732586731,"relation":"main_file","content_type":"application/x-zip-compressed","creator":"alaurits","date_created":"2023-04-26T12:27:34Z","access_level":"open_access","file_name":"simulations_era=10_flux_varied_europe.zip","date_updated":"2023-04-26T12:27:34Z","success":1,"checksum":"25bf79452ae895f9c8a20571a096b4c3"},{"content_type":"application/x-zip-compressed","date_created":"2023-04-26T12:29:53Z","creator":"alaurits","access_level":"open_access","file_id":"12872","relation":"main_file","file_size":1743893150,"success":1,"checksum":"bca48d80ece73eb169aee7211a4a751a","file_name":"simulations_era=10_flux_varied_torus.zip","date_updated":"2023-04-26T12:29:53Z"},{"checksum":"e77a655db15486a387a36362fbf0b665","success":1,"file_name":"simulations_era=10_R_varied_torus.zip","date_updated":"2023-04-26T12:29:19Z","date_created":"2023-04-26T12:29:19Z","creator":"alaurits","access_level":"open_access","content_type":"application/x-zip-compressed","file_size":878391851,"relation":"main_file","file_id":"12873"},{"file_size":201652478,"relation":"main_file","file_id":"12874","creator":"alaurits","date_created":"2023-04-26T12:30:05Z","access_level":"open_access","content_type":"application/x-zip-compressed","file_name":"simulations_era=100.zip","date_updated":"2023-04-26T12:30:05Z","checksum":"8556406513adc4aa2e0417f46680f627","success":1}],"tmp":{"image":"/images/cc_0.png","name":"Creative Commons Public Domain Dedication (CC0 1.0)","short":"CC0 (1.0)","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Klausen, Frederik Ravn","first_name":"Frederik Ravn","last_name":"Klausen"},{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen"}],"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"license":"https://creativecommons.org/publicdomain/zero/1.0/","file_date_updated":"2023-04-26T12:30:06Z","date_created":"2023-04-26T12:34:49Z","acknowledgement":"FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs. ","corr_author":"1","ddc":["000"],"date_updated":"2025-09-09T12:26:01Z","has_accepted_license":"1","status":"public","date_published":"2023-04-26T00:00:00Z","abstract":[{"lang":"eng","text":"We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately round cultures get a competitive advantage.  We first analyse the model  with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e. freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity and the central European plain has less clear cultural borders. "}],"month":"04","article_processing_charge":"No","title":"Research data for: A stochastic cellular automaton model of culture formation","related_material":{"record":[{"relation":"used_in_publication","id":"14505","status":"deleted"},{"relation":"used_in_publication","id":"12890","status":"public"}]},"type":"research_data","day":"26","doi":"10.15479/AT:ISTA:12869","publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","year":"2023","citation":{"ama":"Klausen FR, Lauritsen AB. Research data for: A stochastic cellular automaton model of culture formation. 2023. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:12869\">10.15479/AT:ISTA:12869</a>","chicago":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Research Data for: A Stochastic Cellular Automaton Model of Culture Formation.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/AT:ISTA:12869\">https://doi.org/10.15479/AT:ISTA:12869</a>.","short":"F.R. Klausen, A.B. Lauritsen, (2023).","mla":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. <i>Research Data for: A Stochastic Cellular Automaton Model of Culture Formation</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:12869\">10.15479/AT:ISTA:12869</a>.","apa":"Klausen, F. R., &#38; Lauritsen, A. B. (2023). Research data for: A stochastic cellular automaton model of culture formation. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:12869\">https://doi.org/10.15479/AT:ISTA:12869</a>","ista":"Klausen FR, Lauritsen AB. 2023. Research data for: A stochastic cellular automaton model of culture formation, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:12869\">10.15479/AT:ISTA:12869</a>.","ieee":"F. R. Klausen and A. B. Lauritsen, “Research data for: A stochastic cellular automaton model of culture formation.” Institute of Science and Technology Austria, 2023."},"_id":"12869"},{"article_number":"054307","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"date_created":"2023-05-04T08:35:01Z","publication_identifier":{"eissn":["2470-0053"],"issn":["2470-0045"]},"intvolume":"       108","language":[{"iso":"eng"}],"quality_controlled":"1","external_id":{"arxiv":["2305.02153"],"pmid":["38115445"],"isi":["001106396300005"]},"corr_author":"1","date_updated":"2025-09-09T12:26:01Z","publication":"Physical Review E","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.02153"}],"volume":108,"citation":{"short":"F.R. Klausen, A.B. Lauritsen, Physical Review E 108 (2023).","mla":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” <i>Physical Review E</i>, vol. 108, no. 5, 054307, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">10.1103/PhysRevE.108.054307</a>.","apa":"Klausen, F. R., &#38; Lauritsen, A. B. (2023). Stochastic cellular automaton model of culture formation. <i>Physical Review E</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">https://doi.org/10.1103/PhysRevE.108.054307</a>","ista":"Klausen FR, Lauritsen AB. 2023. Stochastic cellular automaton model of culture formation. Physical Review E. 108(5), 054307.","ieee":"F. R. Klausen and A. B. Lauritsen, “Stochastic cellular automaton model of culture formation,” <i>Physical Review E</i>, vol. 108, no. 5. American Physical Society, 2023.","ama":"Klausen FR, Lauritsen AB. Stochastic cellular automaton model of culture formation. <i>Physical Review E</i>. 2023;108(5). doi:<a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">10.1103/PhysRevE.108.054307</a>","chicago":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” <i>Physical Review E</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">https://doi.org/10.1103/PhysRevE.108.054307</a>."},"related_material":{"link":[{"url":"https://github.com/FrederikRavnKlausen/model-for-culture-formation","relation":"software"}],"record":[{"id":"12869","relation":"research_data","status":"public"}]},"type":"journal_article","day":"08","publisher":"American Physical Society","doi":"10.1103/PhysRevE.108.054307","author":[{"first_name":"Frederik Ravn","full_name":"Klausen, Frederik Ravn","last_name":"Klausen"},{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","orcid":"0000-0003-4476-2288"}],"publication_status":"published","article_type":"original","oa":1,"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","scopus_import":"1","date_published":"2023-11-08T00:00:00Z","abstract":[{"text":"We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately geometrically round cultures get a competitive advantage. We first analyze the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e., freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely, that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity, and the central European plain has less clear cultural borders.","lang":"eng"}],"acknowledgement":"Thanks to Kim Sneppen, Svend Krøjer, Peter Wildemann, Peter Rasmussen and Kent Bækgaard Lauritsen for discussions and suggestions. FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs.","arxiv":1,"article_processing_charge":"No","month":"11","pmid":1,"oa_version":"Preprint","year":"2023","_id":"12890","issue":"5","title":"Stochastic cellular automaton model of culture formation"},{"external_id":{"arxiv":["2106.11217"],"isi":["000990804300001"]},"date_updated":"2025-04-15T08:31:52Z","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"intvolume":"       285","quality_controlled":"1","language":[{"iso":"eng"}],"article_number":"109963","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"date_created":"2023-05-07T22:01:02Z","related_material":{"record":[{"id":"9792","relation":"earlier_version","status":"public"}]},"type":"journal_article","ec_funded":1,"day":"15","doi":"10.1016/j.jfa.2023.109963","publisher":"Elsevier","volume":285,"citation":{"apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>","ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. 2023;285(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2106.11217","open_access":"1"}],"publication":"Journal of Functional Analysis","acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","arxiv":1,"status":"public","date_published":"2023-08-15T00:00:00Z","abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"scopus_import":"1","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","orcid":"0000-0003-0754-8530"},{"last_name":"Gerolin","first_name":"Augusto","full_name":"Gerolin, Augusto"},{"last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"grant_number":"F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Taming Complexity in Partial Differential Systems"}],"publication_status":"published","article_type":"original","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","oa_version":"Preprint","year":"2023","_id":"12911","issue":"4","month":"08","article_processing_charge":"No"},{"publication_status":"published","article_type":"original","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Mitrouskas","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes"},{"full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof","last_name":"Mysliwy"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"isi":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","creator":"alisjak","date_created":"2023-07-03T10:36:25Z","content_type":"application/pdf","file_size":943192,"relation":"main_file","file_id":"13186","checksum":"f672eb7dd015c472c9a04f1b9bf9df7d","success":1,"date_updated":"2023-07-03T10:36:25Z","file_name":"2023_ForumofMathematics.Sigma_Mitrouskas.pdf"}],"oa":1,"abstract":[{"lang":"eng","text":"We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar."}],"date_published":"2023-06-13T00:00:00Z","scopus_import":"1","status":"public","ddc":["500"],"arxiv":1,"acknowledgement":"This research was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.).","article_processing_charge":"Yes","month":"06","_id":"13178","year":"2023","oa_version":"Published Version","title":"Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron","file_date_updated":"2023-07-03T10:36:25Z","date_created":"2023-07-02T22:00:43Z","department":[{"_id":"RoSe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        11","publication_identifier":{"eissn":["2050-5094"]},"has_accepted_license":"1","date_updated":"2025-04-14T07:26:58Z","corr_author":"1","external_id":{"arxiv":["2203.02454"],"isi":["001005008800001"]},"publication":"Forum of Mathematics","citation":{"ama":"Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. <i>Forum of Mathematics</i>. 2023;11:1-52. doi:<a href=\"https://doi.org/10.1017/fms.2023.45\">10.1017/fms.2023.45</a>","chicago":"Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” <i>Forum of Mathematics</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.45\">https://doi.org/10.1017/fms.2023.45</a>.","short":"D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023) 1–52.","ieee":"D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron,” <i>Forum of Mathematics</i>, vol. 11. Cambridge University Press, pp. 1–52, 2023.","apa":"Mitrouskas, D. J., Mysliwy, K., &#38; Seiringer, R. (2023). Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. <i>Forum of Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.45\">https://doi.org/10.1017/fms.2023.45</a>","ista":"Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. 11, 1–52.","mla":"Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” <i>Forum of Mathematics</i>, vol. 11, Cambridge University Press, 2023, pp. 1–52, doi:<a href=\"https://doi.org/10.1017/fms.2023.45\">10.1017/fms.2023.45</a>."},"volume":11,"publisher":"Cambridge University Press","doi":"10.1017/fms.2023.45","day":"13","page":"1-52","ec_funded":1,"type":"journal_article"},{"type":"journal_article","ec_funded":1,"doi":"10.1007/s00205-023-01893-6","publisher":"Springer Nature","day":"01","volume":247,"citation":{"ama":"Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(4). doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>","chicago":"Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>.","short":"N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023).","ieee":"N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas with large interaction potential,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4. Springer Nature, 2023.","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 4, 65, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01893-6\">10.1007/s00205-023-01893-6</a>.","ista":"Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 247(4), 65.","apa":"Benedikter, N. P., Porta, M., Schlein, B., &#38; Seiringer, R. (2023). Correlation energy of a weakly interacting Fermi gas with large interaction potential. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01893-6\">https://doi.org/10.1007/s00205-023-01893-6</a>"},"publication":"Archive for Rational Mechanics and Analysis","external_id":{"arxiv":["2106.13185"],"isi":["001024369000001"]},"date_updated":"2025-04-14T07:26:58Z","has_accepted_license":"1","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"intvolume":"       247","language":[{"iso":"eng"}],"quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"65","department":[{"_id":"RoSe"}],"file_date_updated":"2023-11-14T13:12:12Z","date_created":"2023-07-16T22:01:08Z","title":"Correlation energy of a weakly interacting Fermi gas with large interaction potential","oa_version":"Published Version","year":"2023","issue":"4","_id":"13225","month":"08","article_processing_charge":"Yes (via OA deal)","acknowledgement":"RS was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227). MP acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement.","arxiv":1,"ddc":["510"],"status":"public","abstract":[{"lang":"eng","text":"Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy."}],"scopus_import":"1","date_published":"2023-08-01T00:00:00Z","oa":1,"file":[{"creator":"dernst","date_created":"2023-11-14T13:12:12Z","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":851626,"file_id":"14535","checksum":"2b45828d854a253b14bf7aa196ec55e9","success":1,"file_name":"2023_ArchiveRationalMechAnalysis_Benedikter.pdf","date_updated":"2023-11-14T13:12:12Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"author":[{"first_name":"Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","full_name":"Benedikter, Niels P","orcid":"0000-0002-1071-6091","last_name":"Benedikter"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"article_type":"original","publication_status":"published"},{"citation":{"short":"L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023).","apa":"Bossmann, L., &#38; Petrat, S. P. (2023). Weak Edgeworth expansion for the mean-field Bose gas. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-023-01698-4\">https://doi.org/10.1007/s11005-023-01698-4</a>","ista":"Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77.","mla":"Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4, 77, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s11005-023-01698-4\">10.1007/s11005-023-01698-4</a>.","ieee":"L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field Bose gas,” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4. Springer Nature, 2023.","ama":"Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas. <i>Letters in Mathematical Physics</i>. 2023;113(4). doi:<a href=\"https://doi.org/10.1007/s11005-023-01698-4\">10.1007/s11005-023-01698-4</a>","chicago":"Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11005-023-01698-4\">https://doi.org/10.1007/s11005-023-01698-4</a>."},"volume":113,"publisher":"Springer Nature","doi":"10.1007/s11005-023-01698-4","day":"03","ec_funded":1,"type":"journal_article","publication":"Letters in Mathematical Physics","intvolume":"       113","language":[{"iso":"eng"}],"quality_controlled":"1","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"date_updated":"2025-06-25T06:20:15Z","OA_place":"publisher","has_accepted_license":"1","external_id":{"isi":["001022878900002"],"arxiv":["2208.00199"]},"corr_author":"1","date_created":"2023-07-16T22:01:08Z","file_date_updated":"2025-06-25T06:20:02Z","article_number":"77","department":[{"_id":"RoSe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"year":"2023","_id":"13226","issue":"4","oa_version":"Published Version","title":"Weak Edgeworth expansion for the mean-field Bose gas","article_processing_charge":"Yes (via OA deal)","month":"07","scopus_import":"1","date_published":"2023-07-03T00:00:00Z","abstract":[{"lang":"eng","text":"We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion."}],"status":"public","OA_type":"hybrid","acknowledgement":"It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee for many constructive comments. L.B. gratefully acknowledges funding from the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111) and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen Access funding enabled and organized by Projekt DEAL.","ddc":["510"],"arxiv":1,"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"article_type":"original","publication_status":"published","author":[{"last_name":"Bossmann","orcid":"0000-0002-6854-1343","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","full_name":"Bossmann, Lea"},{"full_name":"Petrat, Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","first_name":"Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat"}],"file":[{"file_size":586698,"relation":"main_file","file_id":"19898","access_level":"open_access","date_created":"2025-06-25T06:20:02Z","creator":"dernst","content_type":"application/pdf","date_updated":"2025-06-25T06:20:02Z","file_name":"2023_LettersMathPhysics_Bossmann.pdf","checksum":"995c902a989a6769fd3db456cfd41111","success":1}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"oa":1},{"page":"973-1008","day":"15","doi":"10.2140/paa.2023.5.973","publisher":"Mathematical Sciences Publishers","type":"journal_article","citation":{"apa":"Mitrouskas, D. J., &#38; Seiringer, R. (2023). Ubiquity of bound states for the strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2023.5.973\">https://doi.org/10.2140/paa.2023.5.973</a>","ista":"Mitrouskas DJ, Seiringer R. 2023. Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. 5(4), 973–1008.","mla":"Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States for the Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>, vol. 5, no. 4, Mathematical Sciences Publishers, 2023, pp. 973–1008, doi:<a href=\"https://doi.org/10.2140/paa.2023.5.973\">10.2140/paa.2023.5.973</a>.","ieee":"D. J. Mitrouskas and R. Seiringer, “Ubiquity of bound states for the strongly coupled polaron,” <i>Pure and Applied Analysis</i>, vol. 5, no. 4. Mathematical Sciences Publishers, pp. 973–1008, 2023.","short":"D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008.","chicago":"Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States for the Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/paa.2023.5.973\">https://doi.org/10.2140/paa.2023.5.973</a>.","ama":"Mitrouskas DJ, Seiringer R. Ubiquity of bound states for the strongly coupled polaron. <i>Pure and Applied Analysis</i>. 2023;5(4):973-1008. doi:<a href=\"https://doi.org/10.2140/paa.2023.5.973\">10.2140/paa.2023.5.973</a>"},"volume":5,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2211.03606"}],"publication":"Pure and Applied Analysis","date_updated":"2025-04-23T14:21:39Z","OA_place":"repository","external_id":{"arxiv":["2211.03606"]},"corr_author":"1","intvolume":"         5","language":[{"iso":"eng"}],"quality_controlled":"1","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"date_created":"2024-01-22T08:24:23Z","department":[{"_id":"RoSe"}],"title":"Ubiquity of bound states for the strongly coupled polaron","keyword":["General Medicine"],"year":"2023","issue":"4","_id":"14854","oa_version":"Preprint","month":"12","article_processing_charge":"No","OA_type":"green","arxiv":1,"abstract":[{"text":"We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math. Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov type.","lang":"eng"}],"date_published":"2023-12-15T00:00:00Z","scopus_import":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"article_type":"original","publication_status":"published","author":[{"last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}]},{"publication":"Density Functional Theory","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.10424","open_access":"1"}],"citation":{"short":"M. Lewin, E.H. Lieb, R. Seiringer, in:, E. Cances, G. Friesecke (Eds.), Density Functional Theory, 1st ed., Springer, 2023, pp. 115–182.","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “Universal Functionals in Density Functional Theory,” in <i>Density Functional Theory</i>, 1st ed., E. Cances and G. Friesecke, Eds. Springer, 2023, pp. 115–182.","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2023). Universal Functionals in Density Functional Theory. In E. Cances &#38; G. Friesecke (Eds.), <i>Density Functional Theory</i> (1st ed., pp. 115–182). Springer. <a href=\"https://doi.org/10.1007/978-3-031-22340-2_3\">https://doi.org/10.1007/978-3-031-22340-2_3</a>","ista":"Lewin M, Lieb EH, Seiringer R. 2023.Universal Functionals in Density Functional Theory. In: Density Functional Theory. Mathematics and Molecular Modeling, , 115–182.","mla":"Lewin, Mathieu, et al. “Universal Functionals in Density Functional Theory.” <i>Density Functional Theory</i>, edited by Eric Cances and Gero Friesecke, 1st ed., Springer, 2023, pp. 115–82, doi:<a href=\"https://doi.org/10.1007/978-3-031-22340-2_3\">10.1007/978-3-031-22340-2_3</a>.","ama":"Lewin M, Lieb EH, Seiringer R. Universal Functionals in Density Functional Theory. In: Cances E, Friesecke G, eds. <i>Density Functional Theory</i>. 1st ed. MAMOMO. Springer; 2023:115-182. doi:<a href=\"https://doi.org/10.1007/978-3-031-22340-2_3\">10.1007/978-3-031-22340-2_3</a>","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Universal Functionals in Density Functional Theory.” In <i>Density Functional Theory</i>, edited by Eric Cances and Gero Friesecke, 1st ed., 115–82. MAMOMO. Springer, 2023. <a href=\"https://doi.org/10.1007/978-3-031-22340-2_3\">https://doi.org/10.1007/978-3-031-22340-2_3</a>."},"type":"book_chapter","day":"19","doi":"10.1007/978-3-031-22340-2_3","publisher":"Springer","page":"115-182","department":[{"_id":"RoSe"}],"series_title":"MAMOMO","date_created":"2024-02-14T14:44:33Z","publication_identifier":{"issn":["3005-0286"],"isbn":["9783031223396"],"eisbn":["9783031223402"]},"quality_controlled":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["1912.10424"]},"editor":[{"full_name":"Cances, Eric","first_name":"Eric","last_name":"Cances"},{"last_name":"Friesecke","full_name":"Friesecke, Gero","first_name":"Gero"}],"date_updated":"2024-02-20T08:33:06Z","alternative_title":["Mathematics and Molecular Modeling"],"article_processing_charge":"No","edition":"1","month":"07","oa_version":"Preprint","_id":"14992","year":"2023","title":"Universal Functionals in Density Functional Theory","author":[{"full_name":"Lewin, Mathieu","first_name":"Mathieu","last_name":"Lewin"},{"full_name":"Lieb, Elliott H.","first_name":"Elliott H.","last_name":"Lieb"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert"}],"publication_status":"published","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","abstract":[{"text":"In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of this functional, corresponding to using mixed canonical and grand-canonical states, respectively. We present some recent works about the local density approximation, in which the functionals get replaced by purely local functionals constructed using the uniform electron gas energy per unit volume. We then review the known upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic energy alone, then turn to the classical interaction alone, before we are able to put everything together. A later section is devoted to the Hohenberg–Kohn theorem and the role of many-body unique continuation in its proof.","lang":"eng"}],"date_published":"2023-07-19T00:00:00Z","arxiv":1},{"acknowledgement":"We are grateful to Rupert Frank for helpful discussions at an early stage of this project.\r\nFunding from the European Union’s Horizon 2020 research and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged.","arxiv":1,"status":"public","abstract":[{"text":"We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy EN is given by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states ΨN, i.e. states satisfying ⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect to one of the Hartree minimizers.","lang":"eng"}],"scopus_import":"1","date_published":"2023-02-21T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Morris","full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","orcid":"0000-0002-6249-0928","last_name":"Brooks"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"article_type":"original","publication_status":"published","title":"Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases","oa_version":"Preprint","year":"2023","_id":"17074","issue":"4","month":"02","article_processing_charge":"No","external_id":{"arxiv":["2111.13864"]},"corr_author":"1","date_updated":"2025-04-14T07:26:59Z","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"intvolume":"         3","quality_controlled":"1","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"date_created":"2024-05-29T06:12:54Z","type":"journal_article","ec_funded":1,"page":"939-1000","publisher":"Mathematical Sciences Publishers","day":"21","doi":"10.2140/pmp.2022.3.939","volume":3,"citation":{"ama":"Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>. 2023;3(4):939-1000. doi:<a href=\"https://doi.org/10.2140/pmp.2022.3.939\">10.2140/pmp.2022.3.939</a>","chicago":"Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/pmp.2022.3.939\">https://doi.org/10.2140/pmp.2022.3.939</a>.","short":"M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000.","ieee":"M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases,” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 939–1000, 2023.","apa":"Brooks, M., &#38; Seiringer, R. (2023). Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2022.3.939\">https://doi.org/10.2140/pmp.2022.3.939</a>","ista":"Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.","mla":"Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:<a href=\"https://doi.org/10.2140/pmp.2022.3.939\">10.2140/pmp.2022.3.939</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2111.13864"}],"publication":"Probability and Mathematical Physics"}]