[{"author":[{"full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","orcid":"0000-0002-6249-0928","first_name":"Morris"},{"last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes"}],"_id":"19372","issue":"1","external_id":{"arxiv":["2306.16373"]},"volume":6,"intvolume":"         6","page":"281-325","article_processing_charge":"No","date_published":"2025-02-23T00:00:00Z","year":"2025","publisher":"Mathematical Sciences Publishers","oa":1,"OA_type":"green","title":" Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"repository","article_type":"original","date_updated":"2025-03-10T07:19:02Z","type":"journal_article","publication_identifier":{"eissn":["2690-1005"],"issn":["2690-0998"]},"date_created":"2025-03-09T23:01:28Z","publication":"Probability and Mathematical Physics","abstract":[{"text":"We consider the confined Fröhlich polaron and establish an asymptotic series for the low-energy eigenvalues in negative powers of the coupling constant. The coefficients of the series are derived through a two-fold perturbation approach, involving expansions around the electron Pekar minimizer and the excitations of the quantum field.","lang":"eng"}],"language":[{"iso":"eng"}],"oa_version":"Preprint","quality_controlled":"1","arxiv":1,"day":"23","doi":"10.2140/pmp.2025.6.281","publication_status":"published","department":[{"_id":"RoSe"}],"corr_author":"1","month":"02","acknowledgement":"M.B. gratefully acknowledges funding from the ERC Advanced Grant ERC-AdG CLaQS, grant agreement n. 83478.","scopus_import":"1","citation":{"chicago":"Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for Low-Energy Excitations of the Fröhlich Polaron at Strong Coupling.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/pmp.2025.6.281\">https://doi.org/10.2140/pmp.2025.6.281</a>.","mla":"Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for Low-Energy Excitations of the Fröhlich Polaron at Strong Coupling.” <i>Probability and Mathematical Physics</i>, vol. 6, no. 1, Mathematical Sciences Publishers, 2025, pp. 281–325, doi:<a href=\"https://doi.org/10.2140/pmp.2025.6.281\">10.2140/pmp.2025.6.281</a>.","short":"M. Brooks, D.J. Mitrouskas, Probability and Mathematical Physics 6 (2025) 281–325.","ista":"Brooks M, Mitrouskas DJ. 2025.  Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling. Probability and Mathematical Physics. 6(1), 281–325.","ieee":"M. Brooks and D. J. Mitrouskas, “ Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling,” <i>Probability and Mathematical Physics</i>, vol. 6, no. 1. Mathematical Sciences Publishers, pp. 281–325, 2025.","apa":"Brooks, M., &#38; Mitrouskas, D. J. (2025).  Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2025.6.281\">https://doi.org/10.2140/pmp.2025.6.281</a>","ama":"Brooks M, Mitrouskas DJ.  Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling. <i>Probability and Mathematical Physics</i>. 2025;6(1):281-325. doi:<a href=\"https://doi.org/10.2140/pmp.2025.6.281\">10.2140/pmp.2025.6.281</a>"},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.16373"}]},{"intvolume":"        63","volume":63,"issue":"6","_id":"17282","external_id":{"pmid":["38947856"],"arxiv":["2209.11149"],"isi":["001258097800003"]},"isi":1,"author":[{"full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","orcid":"0000-0002-6249-0928","first_name":"Morris"},{"orcid":"0000-0002-0845-1338","first_name":"Jan","full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas"}],"ddc":["510"],"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"publisher":"Springer Nature","year":"2024","article_number":"153","date_published":"2024-07-01T00:00:00Z","pmid":1,"article_processing_charge":"Yes (via OA deal)","date_created":"2024-07-21T22:01:01Z","publication":"Calculus of Variations and Partial Differential Equations","publication_identifier":{"eissn":["1432-0835"],"issn":["0944-2669"]},"abstract":[{"text":"Let  X  be a vector field and  Y  be a co-vector field on a smooth manifold  M. Does there exist a smooth Riemannian metric  gαβ  on  M  such that  Yβ=gαβXα ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we show that a finite-dimensional ergodic Lindblad equation admits a gradient flow structure for the von Neumann relative entropy if and only if the condition of BKM-detailed balance holds.","lang":"eng"}],"type":"journal_article","date_updated":"2025-09-08T08:24:51Z","file_date_updated":"2024-07-22T07:05:32Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Characterisation of gradient flows for a given functional","article_type":"original","oa":1,"has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"ista":"Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153.","mla":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 6, 153, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00526-024-02755-z\">10.1007/s00526-024-02755-z</a>.","chicago":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00526-024-02755-z\">https://doi.org/10.1007/s00526-024-02755-z</a>.","short":"M. Brooks, J. Maas, Calculus of Variations and Partial Differential Equations 63 (2024).","ama":"Brooks M, Maas J. Characterisation of gradient flows for a given functional. <i>Calculus of Variations and Partial Differential Equations</i>. 2024;63(6). doi:<a href=\"https://doi.org/10.1007/s00526-024-02755-z\">10.1007/s00526-024-02755-z</a>","apa":"Brooks, M., &#38; Maas, J. (2024). Characterisation of gradient flows for a given functional. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-024-02755-z\">https://doi.org/10.1007/s00526-024-02755-z</a>","ieee":"M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 6. Springer Nature, 2024."},"file":[{"checksum":"a0cf0e0ba2157aabb287cb597be17dac","relation":"main_file","content_type":"application/pdf","access_level":"open_access","success":1,"creator":"dernst","file_size":416622,"date_updated":"2024-07-22T07:05:32Z","file_name":"2024_CalculusVariations_Brooks.pdf","file_id":"17289","date_created":"2024-07-22T07:05:32Z"}],"status":"public","scopus_import":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).J. M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB F65. We thank the anonymous referee for valuable comments on the paper.","department":[{"_id":"JaMa"}],"publication_status":"published","ec_funded":1,"day":"01","doi":"10.1007/s00526-024-02755-z","corr_author":"1","month":"07","language":[{"iso":"eng"}],"oa_version":"Published Version","quality_controlled":"1","arxiv":1},{"status":"public","citation":{"apa":"Brooks, M., &#38; Seiringer, R. (2024). The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass. <i>Publications Mathematiques de l’Institut Des Hautes Etudes Scientifiques</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10240-024-00150-0\">https://doi.org/10.1007/s10240-024-00150-0</a>","ama":"Brooks M, Seiringer R. The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass. <i>Publications Mathematiques de l’Institut des Hautes Etudes Scientifiques</i>. 2024;140:271-309. doi:<a href=\"https://doi.org/10.1007/s10240-024-00150-0\">10.1007/s10240-024-00150-0</a>","ieee":"M. Brooks and R. Seiringer, “The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass,” <i>Publications Mathematiques de l’Institut des Hautes Etudes Scientifiques</i>, vol. 140. Springer Nature, pp. 271–309, 2024.","ista":"Brooks M, Seiringer R. 2024. The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass. Publications Mathematiques de l’Institut des Hautes Etudes Scientifiques. 140, 271–309.","mla":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part II — Energy-Momentum Relation and Effective Mass.” <i>Publications Mathematiques de l’Institut Des Hautes Etudes Scientifiques</i>, vol. 140, Springer Nature, 2024, pp. 271–309, doi:<a href=\"https://doi.org/10.1007/s10240-024-00150-0\">10.1007/s10240-024-00150-0</a>.","chicago":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part II — Energy-Momentum Relation and Effective Mass.” <i>Publications Mathematiques de l’Institut Des Hautes Etudes Scientifiques</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10240-024-00150-0\">https://doi.org/10.1007/s10240-024-00150-0</a>.","short":"M. Brooks, R. Seiringer, Publications Mathematiques de l’Institut Des Hautes Etudes Scientifiques 140 (2024) 271–309."},"file":[{"creator":"dernst","file_size":924342,"date_updated":"2025-01-13T08:13:42Z","file_name":"2024_PublicMathIHES_Brooks.pdf","date_created":"2025-01-13T08:13:42Z","file_id":"18824","checksum":"af3becc50f7534c9409d3ff8b5c47ed6","relation":"main_file","content_type":"application/pdf","access_level":"open_access","success":1}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","month":"12","corr_author":"1","doi":"10.1007/s10240-024-00150-0","day":"01","department":[{"_id":"RoSe"}],"publication_status":"published","arxiv":1,"language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","abstract":[{"text":"We study the Fröhlich polaron model in R3, and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper bound proved earlier (Mitrouskas et al. in Forum Math. Sigma 11:1–52, 2023), it shows that the energy is approximately parabolic below the continuum threshold, and that the polaron’s effective mass (defined as the semi-latus rectum of the\r\nparabola) is given by the celebrated Landau–Pekar formula. In particular, it diverges as α4 for large coupling constant α.","lang":"eng"}],"publication_identifier":{"eissn":["1618-1913"],"issn":["0073-8301"]},"date_created":"2024-09-01T22:01:08Z","publication":"Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques","file_date_updated":"2025-01-13T08:13:42Z","date_updated":"2025-09-08T09:08:36Z","type":"journal_article","OA_place":"publisher","article_type":"original","OA_type":"hybrid","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass","has_accepted_license":"1","oa":1,"publisher":"Springer Nature","ddc":["510"],"year":"2024","date_published":"2024-12-01T00:00:00Z","article_processing_charge":"Yes (in subscription journal)","page":"271-309","intvolume":"       140","volume":140,"_id":"17478","external_id":{"isi":["001297785000001"],"arxiv":["2211.03353"]},"author":[{"first_name":"Morris","orcid":"0000-0002-6249-0928","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","last_name":"Brooks"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"isi":1},{"intvolume":"       404","volume":404,"_id":"14441","external_id":{"arxiv":["2207.03156"],"isi":["001096217400007"]},"isi":1,"author":[{"full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","orcid":"0000-0002-6249-0928","first_name":"Morris"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"publisher":"Springer Nature","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"ddc":["510"],"year":"2023","date_published":"2023-11-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","page":"287-337","abstract":[{"lang":"eng","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."}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication":"Communications in Mathematical Physics","date_created":"2023-10-22T22:01:13Z","file_date_updated":"2023-10-31T12:21:39Z","date_updated":"2025-09-09T13:12:02Z","type":"journal_article","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy","oa":1,"has_accepted_license":"1","status":"public","citation":{"short":"M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337.","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>.","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>.","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.","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.","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>","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>"},"file":[{"content_type":"application/pdf","checksum":"1ae49b39247cb6b40ff75997381581b8","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2023-10-31T12:21:39Z","creator":"dernst","file_size":832375,"file_id":"14477","date_created":"2023-10-31T12:21:39Z","file_name":"2023_CommMathPhysics_Brooks.pdf"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","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).","month":"11","corr_author":"1","day":"01","ec_funded":1,"doi":"10.1007/s00220-023-04841-3","department":[{"_id":"RoSe"}],"publication_status":"published","arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Published Version"},{"article_type":"original","title":"Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"abstract":[{"lang":"eng","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."}],"publication":"Probability and Mathematical Physics","date_created":"2024-05-29T06:12:54Z","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"type":"journal_article","date_updated":"2025-04-14T07:26:59Z","month":"02","corr_author":"1","department":[{"_id":"RoSe"}],"publication_status":"published","day":"21","doi":"10.2140/pmp.2022.3.939","ec_funded":1,"arxiv":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2111.13864"}],"status":"public","citation":{"ista":"Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.","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>.","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>.","short":"M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000.","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>","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>","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."},"scopus_import":"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.","external_id":{"arxiv":["2111.13864"]},"_id":"17074","issue":"4","author":[{"first_name":"Morris","orcid":"0000-0002-6249-0928","last_name":"Brooks","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"         3","volume":3,"date_published":"2023-02-21T00:00:00Z","article_processing_charge":"No","page":"939-1000","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"publisher":"Mathematical Sciences Publishers","year":"2023"},{"ddc":["500"],"publisher":"Institute of Science and Technology Austria","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"degree_awarded":"PhD","year":"2022","date_published":"2022-12-15T00:00:00Z","page":"196","article_processing_charge":"No","_id":"12390","alternative_title":["ISTA Thesis"],"author":[{"orcid":"0000-0002-6249-0928","first_name":"Morris","full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks"}],"file":[{"date_updated":"2023-01-26T10:02:34Z","creator":"cchlebak","file_size":3095225,"file_id":"12391","date_created":"2023-01-26T10:02:34Z","file_name":"Brooks_Thesis.pdf","content_type":"application/pdf","checksum":"b31460e937f33b557abb40ebef02b567","relation":"main_file","access_level":"open_access","success":1},{"access_level":"closed","content_type":"application/octet-stream","relation":"source_file","checksum":"9751869fa5e7981588ad4228f4fd4bd6","date_created":"2023-01-26T10:02:42Z","file_id":"12392","file_name":"Brooks_Thesis.tex","date_updated":"2023-01-26T10:02:42Z","file_size":809842,"creator":"cchlebak"}],"citation":{"chicago":"Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively Broken Symmetry.” Institute of Science and Technology Austria, 2022. <a href=\"https://doi.org/10.15479/at:ista:12390\">https://doi.org/10.15479/at:ista:12390</a>.","mla":"Brooks, Morris. <i>Translation-Invariant Quantum Systems with Effectively Broken Symmetry</i>. Institute of Science and Technology Austria, 2022, doi:<a href=\"https://doi.org/10.15479/at:ista:12390\">10.15479/at:ista:12390</a>.","short":"M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken Symmetry, Institute of Science and Technology Austria, 2022.","ista":"Brooks M. 2022. Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria.","ieee":"M. Brooks, “Translation-invariant quantum systems with effectively broken symmetry,” Institute of Science and Technology Austria, 2022.","ama":"Brooks M. Translation-invariant quantum systems with effectively broken symmetry. 2022. doi:<a href=\"https://doi.org/10.15479/at:ista:12390\">10.15479/at:ista:12390</a>","apa":"Brooks, M. (2022). <i>Translation-invariant quantum systems with effectively broken symmetry</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:12390\">https://doi.org/10.15479/at:ista:12390</a>"},"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"status":"public","ec_funded":1,"doi":"10.15479/at:ista:12390","day":"15","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"publication_status":"published","corr_author":"1","month":"12","related_material":{"record":[{"id":"9005","relation":"part_of_dissertation","status":"public"}]},"language":[{"iso":"eng"}],"oa_version":"Published Version","publication_identifier":{"issn":["2663-337X"]},"supervisor":[{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"date_created":"2023-01-26T10:00:42Z","abstract":[{"text":"The scope of this thesis is to study quantum systems exhibiting a continuous symmetry that\r\nis broken on the level of the corresponding effective theory. In particular we are going to\r\ninvestigate translation-invariant Bose gases in the mean field limit, effectively described by\r\nthe Hartree functional, and the Fröhlich Polaron in the regime of strong coupling, effectively\r\ndescribed by the Pekar functional. The latter is a model describing the interaction between a\r\ncharged particle and the optical modes of a polar crystal. Regarding the former, we assume in\r\naddition that the particles in the gas are unconfined, and typically we will consider particles\r\nthat are subject to an attractive interaction. In both cases the ground state energy of the\r\nHamiltonian is not a proper eigenvalue due to the underlying translation-invariance, while on\r\nthe contrary there exists a whole invariant orbit of minimizers for the corresponding effective\r\nfunctionals. Both, the absence of proper eigenstates and the broken symmetry of the effective\r\ntheory, make the study significantly more involved and it is the content of this thesis to\r\ndevelop a frameworks which allows for a systematic way to circumvent these issues.\r\nIt is a well-established result that the ground state energy of Bose gases in the mean field limit,\r\nas well as the ground state energy of the Fröhlich Polaron in the regime of strong coupling, is\r\nto leading order given by the minimal energy of the corresponding effective theory. As part\r\nof this thesis we identify the sub-leading term in the expansion of the ground state energy,\r\nwhich can be interpreted as the quantum correction to the classical energy, since the effective\r\ntheories under consideration can be seen as classical counterparts.\r\nWe are further going to establish an asymptotic expression for the energy-momentum relation\r\nof the Fröhlich Polaron in the strong coupling limit. In the regime of suitably small momenta,\r\nthis asymptotic expression agrees with the energy-momentum relation of a free particle having\r\nan effectively increased mass, and we find that this effectively increased mass agrees with the\r\nconjectured value in the physics literature.\r\nIn addition we will discuss two unrelated papers written by the author during his stay at ISTA\r\nin the appendix. The first one concerns the realization of anyons, which are quasi-particles\r\nacquiring a non-trivial phase under the exchange of two particles, as molecular impurities.\r\nThe second one provides a classification of those vector fields defined on a given manifold\r\nthat can be written as the gradient of a given functional with respect to a suitable metric,\r\nprovided that some mild smoothness assumptions hold. This classification is subsequently\r\nused to identify those quantum Markov semigroups that can be written as a gradient flow of\r\nthe relative entropy.\r\n","lang":"eng"}],"date_updated":"2026-04-16T08:20:52Z","type":"dissertation","file_date_updated":"2023-01-26T10:02:42Z","title":"Translation-invariant quantum systems with effectively broken symmetry","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","OA_place":"publisher","has_accepted_license":"1","oa":1},{"abstract":[{"text":"Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle","lang":"eng"}],"publication":"Atoms","date_created":"2022-01-02T23:01:33Z","publication_identifier":{"eissn":["2218-2004"]},"file_date_updated":"2022-01-03T10:15:05Z","type":"journal_article","date_updated":"2024-10-09T21:01:20Z","article_type":"original","title":"Emergence of anyons on the two-sphere in molecular impurities","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","keyword":["anyons","quasiparticles","Quantum Hall Effect","topological states of matter"],"has_accepted_license":"1","oa":1,"status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"short":"M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Atoms 9 (2021).","chicago":"Brooks, Morris, Mikhail Lemeshko, Douglas Lundholm, and Enderalp Yakaboylu. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” <i>Atoms</i>. MDPI, 2021. <a href=\"https://doi.org/10.3390/atoms9040106\">https://doi.org/10.3390/atoms9040106</a>.","mla":"Brooks, Morris, et al. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” <i>Atoms</i>, vol. 9, no. 4, 106, MDPI, 2021, doi:<a href=\"https://doi.org/10.3390/atoms9040106\">10.3390/atoms9040106</a>.","ista":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 9(4), 106.","ieee":"M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Emergence of anyons on the two-sphere in molecular impurities,” <i>Atoms</i>, vol. 9, no. 4. MDPI, 2021.","apa":"Brooks, M., Lemeshko, M., Lundholm, D., &#38; Yakaboylu, E. (2021). Emergence of anyons on the two-sphere in molecular impurities. <i>Atoms</i>. MDPI. <a href=\"https://doi.org/10.3390/atoms9040106\">https://doi.org/10.3390/atoms9040106</a>","ama":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Emergence of anyons on the two-sphere in molecular impurities. <i>Atoms</i>. 2021;9(4). doi:<a href=\"https://doi.org/10.3390/atoms9040106\">10.3390/atoms9040106</a>"},"file":[{"file_size":303070,"creator":"alisjak","date_updated":"2022-01-03T10:15:05Z","file_name":"2021_Atoms_Brooks.pdf","file_id":"10592","date_created":"2022-01-03T10:15:05Z","relation":"main_file","checksum":"d0e44b95f36c9e06724f66832af0f8c3","content_type":"application/pdf","success":1,"access_level":"open_access"}],"scopus_import":"1","acknowledgement":"D. Lundholm acknowledges financial support from the Göran Gustafsson Foundation (grant no. 1804).","corr_author":"1","month":"12","publication_status":"published","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"day":"02","doi":"10.3390/atoms9040106","arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","intvolume":"         9","volume":9,"external_id":{"arxiv":["2108.06966"]},"_id":"10585","issue":"4","author":[{"first_name":"Morris","orcid":"0000-0002-6249-0928","last_name":"Brooks","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris"},{"last_name":"Lemeshko","full_name":"Lemeshko, Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802","first_name":"Mikhail"},{"first_name":"Douglas","full_name":"Lundholm, Douglas","last_name":"Lundholm"},{"first_name":"Enderalp","orcid":"0000-0001-5973-0874","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","full_name":"Yakaboylu, Enderalp","last_name":"Yakaboylu"}],"publisher":"MDPI","ddc":["530"],"year":"2021","article_number":"106","date_published":"2021-12-02T00:00:00Z","article_processing_charge":"Yes"},{"publisher":"American Physical Society","project":[{"grant_number":"801770","name":"Angulon: physics and applications of a new quasiparticle","call_identifier":"H2020","_id":"2688CF98-B435-11E9-9278-68D0E5697425"}],"article_number":"015301","year":"2021","date_published":"2021-01-08T00:00:00Z","pmid":1,"article_processing_charge":"No","intvolume":"       126","volume":126,"_id":"9005","issue":"1","external_id":{"isi":["000606325000003"],"arxiv":["2009.05948"],"pmid":["33480760"]},"author":[{"full_name":"Brooks, Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","orcid":"0000-0002-6249-0928","first_name":"Morris"},{"first_name":"Mikhail","orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Lemeshko, Mikhail","last_name":"Lemeshko"},{"first_name":"D.","full_name":"Lundholm, D.","last_name":"Lundholm"},{"first_name":"Enderalp","orcid":"0000-0001-5973-0874","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","full_name":"Yakaboylu, Enderalp","last_name":"Yakaboylu"}],"isi":1,"status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2009.05948","open_access":"1"}],"citation":{"short":"M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Physical Review Letters 126 (2021).","chicago":"Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” <i>Physical Review Letters</i>. American Physical Society, 2021. <a href=\"https://doi.org/10.1103/PhysRevLett.126.015301\">https://doi.org/10.1103/PhysRevLett.126.015301</a>.","mla":"Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” <i>Physical Review Letters</i>, vol. 126, no. 1, 015301, American Physical Society, 2021, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.126.015301\">10.1103/PhysRevLett.126.015301</a>.","ista":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 126(1), 015301.","ieee":"M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities as a realization of anyons on the two-sphere,” <i>Physical Review Letters</i>, vol. 126, no. 1. American Physical Society, 2021.","apa":"Brooks, M., Lemeshko, M., Lundholm, D., &#38; Yakaboylu, E. (2021). Molecular impurities as a realization of anyons on the two-sphere. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.126.015301\">https://doi.org/10.1103/PhysRevLett.126.015301</a>","ama":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization of anyons on the two-sphere. <i>Physical Review Letters</i>. 2021;126(1). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.126.015301\">10.1103/PhysRevLett.126.015301</a>"},"acknowledgement":"We are grateful to A. Ghazaryan for valuable discussions and also thank the anonymous referees for comments. D.L. acknowledges financial support from the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully acknowledges financial support\r\nby the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 801770).","scopus_import":"1","month":"01","related_material":{"record":[{"relation":"dissertation_contains","id":"12390","status":"public"}],"link":[{"relation":"press_release","url":"https://ist.ac.at/en/news/dancing-molecules-and-two-dimensional-particles/","description":"News on IST Homepage"}]},"doi":"10.1103/PhysRevLett.126.015301","day":"08","ec_funded":1,"publication_status":"published","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"arxiv":1,"oa_version":"Preprint","quality_controlled":"1","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field."}],"publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"date_created":"2021-01-17T23:01:10Z","publication":"Physical Review Letters","date_updated":"2026-04-16T08:20:53Z","type":"journal_article","article_type":"original","title":"Molecular impurities as a realization of anyons on the two-sphere","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1},{"citation":{"ama":"Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite dimension. <i>Journal of Functional Analysis</i>. 2021;281(3). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">10.1016/j.jfa.2021.109029</a>","apa":"Brooks, M., &#38; Di Gesù, G. (2021). Sharp tunneling estimates for a double-well model in infinite dimension. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">https://doi.org/10.1016/j.jfa.2021.109029</a>","ieee":"M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model in infinite dimension,” <i>Journal of Functional Analysis</i>, vol. 281, no. 3. Elsevier, 2021.","ista":"Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 281(3), 109029.","mla":"Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>, vol. 281, no. 3, 109029, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">10.1016/j.jfa.2021.109029</a>.","short":"M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021).","chicago":"Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">https://doi.org/10.1016/j.jfa.2021.109029</a>."},"main_file_link":[{"url":"https://arxiv.org/abs/1911.03187","open_access":"1"}],"status":"public","acknowledgement":"GDG gratefully acknowledges the financial support of HIM Bonn in the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness, PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La Sapienza during his frequent visits.","scopus_import":"1","publication_status":"published","department":[{"_id":"RoSe"}],"day":"07","doi":"10.1016/j.jfa.2021.109029","month":"04","oa_version":"Preprint","quality_controlled":"1","language":[{"iso":"eng"}],"arxiv":1,"publication":"Journal of Functional Analysis","date_created":"2021-04-25T22:01:29Z","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"abstract":[{"lang":"eng","text":"We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension."}],"type":"journal_article","date_updated":"2023-08-08T13:15:11Z","title":"Sharp tunneling estimates for a double-well model in infinite dimension","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","oa":1,"publisher":"Elsevier","year":"2021","article_number":"109029","date_published":"2021-04-07T00:00:00Z","article_processing_charge":"No","intvolume":"       281","volume":281,"issue":"3","_id":"9348","external_id":{"arxiv":["1911.03187"],"isi":["000644702800005"]},"author":[{"first_name":"Morris","orcid":"0000-0002-6249-0928","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","last_name":"Brooks"},{"full_name":"Di Gesù, Giacomo","last_name":"Di Gesù","first_name":"Giacomo"}],"isi":1}]