[{"has_accepted_license":"1","oa":1,"ddc":["500"],"external_id":{"arxiv":["2409.17297"]},"language":[{"iso":"eng"}],"das_tickbox":"1","_id":"22290","author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"full_name":"Langmann, Edwin","last_name":"Langmann","first_name":"Edwin"},{"full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard"}],"abstract":[{"text":"We introduce a multi-band BCS free energy functional and prove that for a multi-band superconductor the effect of inter-band coupling can only increase the critical temperature, irrespective of its attractive or repulsive nature and its strength. Further, for weak coupling and weaker inter-band coupling, we prove that the dependence of the increase in critical temperature on the inter-band coupling is (1) linear, if there are two or more equally strongly superconducting bands, or (2) quadratic, if there is only one dominating band.","lang":"eng"}],"department":[{"_id":"LaEr"},{"_id":"RoSe"}],"researchdata_availability":"not applicable","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00023-026-01706-y","dataavailabilitystatement":"Data sharing is not applicable to this article as no new data were created or analyzed in this study.","fulldoi":"https://doi.org/10.1007/s00023-026-01706-y","supplementarymaterial":"not applicable","year":"2026","publisher":"Springer Nature","month":"06","main_file_link":[{"url":"https://doi.org/10.1007/s00023-026-01706-y","open_access":"1"}],"date_updated":"2026-07-13T11:34:08Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Annales Henri Poincaré","publication_status":"epub_ahead","OA_type":"hybrid","OA_place":"publisher","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"quality_controlled":"1","PlanS_conform":"1","date_published":"2026-06-29T00:00:00Z","oa_version":"Published Version","title":"Multi-band superconductors have enhanced critical temperatures","ec_funded":1,"article_type":"original","arxiv":1,"day":"29","date_created":"2026-07-13T09:42:22Z","scopus_import":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"type":"journal_article","related_material":{"record":[{"id":"19550","relation":"earlier_version","status":"public"}]},"acknowledgement":"We would like to thank J. Lenells and R. Seiringer for their interest and helpful discussions, E. Babaev and Y. Yerin for useful comments about the literature, and the anonymous referee for their comments. J.H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331 and the ERC Consollidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education, Research and Innovation). E.L. gratefully acknowledges support from the Swedish Research Council, Grant No. 2023-04726. A.B.L. gratefully acknowledges partial financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) and by the French State support managed by ANR under the France 2030 program through the MaQuI CNRS Risky and High-Impact Research programme (RI)^2 (grant agreement ANR-24-RRII-0001). Open access funding provided by Royal Institute of Technology.","citation":{"mla":"Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>Annales Henri Poincaré</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00023-026-01706-y\">10.1007/s00023-026-01706-y</a>.","chicago":"Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>Annales Henri Poincaré</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00023-026-01706-y\">https://doi.org/10.1007/s00023-026-01706-y</a>.","ama":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. <i>Annales Henri Poincaré</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s00023-026-01706-y\">10.1007/s00023-026-01706-y</a>","ista":"Henheik SJ, Langmann E, Lauritsen AB. 2026. Multi-band superconductors have enhanced critical temperatures. Annales Henri Poincaré.","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>Annales Henri Poincaré</i>. Springer Nature, 2026.","apa":"Henheik, S. J., Langmann, E., &#38; Lauritsen, A. B. (2026). Multi-band superconductors have enhanced critical temperatures. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-026-01706-y\">https://doi.org/10.1007/s00023-026-01706-y</a>","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026)."},"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}]},{"oa_version":"Published Version","title":"Density of small singular values of the shifted real Ginibre ensemble","date_published":"2022-11-01T00:00:00Z","quality_controlled":"1","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"status":"public","publication":"Annales Henri Poincaré","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>."},"acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"type":"journal_article","isi":1,"article_type":"original","date_created":"2023-01-16T09:50:26Z","day":"01","scopus_import":"1","doi":"10.1007/s00023-022-01188-8","abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"department":[{"_id":"LaEr"}],"article_processing_charge":"No","page":"3981-4002","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"issue":"11","_id":"12232","external_id":{"isi":["000796323500001"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","oa":1,"intvolume":"        23","ddc":["510"],"file":[{"date_created":"2023-01-27T11:06:47Z","creator":"dernst","file_id":"12424","content_type":"application/pdf","relation":"main_file","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","success":1,"access_level":"open_access","date_updated":"2023-01-27T11:06:47Z","checksum":"5582f059feeb2f63e2eb68197a34d7dc","file_size":1333638}],"file_date_updated":"2023-01-27T11:06:47Z","date_updated":"2023-08-04T09:33:52Z","volume":23,"month":"11","year":"2022","publisher":"Springer Nature","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"fulldoi":"https://doi.org/10.1007/s00023-022-01188-8"},{"date_updated":"2025-04-15T08:04:59Z","file":[{"file_size":1162454,"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","date_updated":"2022-05-12T12:50:27Z","access_level":"open_access","success":1,"file_name":"2021_AnnHenriPoincare_Erdoes.pdf","relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"11365","date_created":"2022-05-12T12:50:27Z"}],"file_date_updated":"2022-05-12T12:50:27Z","publisher":"Springer Nature","month":"12","year":"2021","volume":22,"fulldoi":"https://doi.org/10.1007/s00023-021-01085-6","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"last_name":"Nemish","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy"}],"page":"4205–4269","doi":"10.1007/s00023-021-01085-6","article_processing_charge":"Yes (in subscription journal)","department":[{"_id":"LaEr"}],"abstract":[{"text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.","lang":"eng"}],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"ddc":["510"],"has_accepted_license":"1","intvolume":"        22","oa":1,"_id":"9912","acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"citation":{"ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” <i>Annales Henri Poincaré </i>, vol. 22. Springer Nature, pp. 4205–4269, 2021.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>.","mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>.","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>"},"isi":1,"date_created":"2021-08-15T22:01:29Z","scopus_import":"1","day":"01","article_type":"original","arxiv":1,"type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"quality_controlled":"1","ec_funded":1,"title":"Scattering in quantum dots via noncommutative rational functions","oa_version":"Published Version","date_published":"2021-12-01T00:00:00Z","publication":"Annales Henri Poincaré ","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","status":"public","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]}},{"publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"OA_place":"publisher","OA_type":"hybrid","publication_status":"published","publication":"Annales Henri Poincare","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","ec_funded":1,"title":"Mean-field dynamics for the Nelson model with fermions","oa_version":"Published Version","date_published":"2019-10-01T00:00:00Z","quality_controlled":"1","type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"isi":1,"corr_author":"1","day":"01","scopus_import":"1","date_created":"2019-08-11T21:59:21Z","arxiv":1,"article_type":"original","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"citation":{"chicago":"Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>.","mla":"Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” <i>Annales Henri Poincare</i>, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>.","ama":"Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. 2019;20(10):3471–3508. doi:<a href=\"https://doi.org/10.1007/s00023-019-00828-w\">10.1007/s00023-019-00828-w</a>","ieee":"N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” <i>Annales Henri Poincare</i>, vol. 20, no. 10. Springer Nature, pp. 3471–3508, 2019.","ista":"Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508.","short":"N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508.","apa":"Leopold, N. K., &#38; Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-019-00828-w\">https://doi.org/10.1007/s00023-019-00828-w</a>"},"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). We would like to thank Peter Pickl and Robert Seiringer for fruitful discussions, and the anonymous referees for their valuable comments and suggestions. Moreover, we would like to thank Niels Benedikter and László Erdős for helpful remarks about the semiclassical structure and the Schrödinger–Klein–Gordon equations. N. L. gratefully acknowledges financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 694227) and funding for his stay at Princeton University from the project “Effective One-Particle Equations for Correlated Many-Particle-(Coulomb) Systems: Derivation and Properties” (Project No. 318342445) of the German Research Foundation (DFG). S. P. gratefully acknowledges support from the German Academic Exchange Service (DAAD) and the National Science Foundation under Agreement No. DMS-1128155. Moreover, we would like to thank Princeton University and the Institute for Advanced Study for their hospitality. S. P. would additionally like to thank the University of Washington for hospitality.","issue":"10","_id":"6788","language":[{"iso":"eng"}],"external_id":{"arxiv":["1807.06781"],"isi":["000487036900008"]},"ddc":["510"],"oa":1,"intvolume":"        20","has_accepted_license":"1","doi":"10.1007/s00023-019-00828-w","article_processing_charge":"Yes (via OA deal)","abstract":[{"lang":"eng","text":"We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations."}],"department":[{"_id":"RoSe"}],"author":[{"full_name":"Leopold, Nikolai K","last_name":"Leopold","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","orcid":"0000-0002-0495-6822"},{"last_name":"Petrat","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9166-5889","full_name":"Petrat, Sören P"}],"page":"3471–3508","month":"10","publisher":"Springer Nature","year":"2019","volume":20,"fulldoi":"https://doi.org/10.1007/s00023-019-00828-w","file":[{"file_size":681139,"checksum":"b6dbf0d837d809293d449adf77138904","date_updated":"2020-07-14T12:47:40Z","access_level":"open_access","file_name":"2019_AnnalesHenriPoincare_Leopold.pdf","relation":"main_file","file_id":"6801","creator":"dernst","content_type":"application/pdf","date_created":"2019-08-12T12:05:58Z"}],"file_date_updated":"2020-07-14T12:47:40Z","date_updated":"2026-07-28T13:24:14Z"},{"title":"Existence of the D0-D4 bound state: A detailed proof","oa_version":"None","date_published":"2005-04-01T00:00:00Z","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"status":"public","publication":"Annales Henri Poincare","publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ieee":"L. Erdös, D. Hasler, and J. Solovej, “Existence of the D0-D4 bound state: A detailed proof,” <i>Annales Henri Poincare</i>, vol. 6, no. 2. Birkhäuser, pp. 247–267, 2005.","ista":"Erdös L, Hasler D, Solovej J. 2005. Existence of the D0-D4 bound state: A detailed proof. Annales Henri Poincare. 6(2), 247–267.","short":"L. Erdös, D. Hasler, J. Solovej, Annales Henri Poincare 6 (2005) 247–267.","apa":"Erdös, L., Hasler, D., &#38; Solovej, J. (2005). Existence of the D0-D4 bound state: A detailed proof. <i>Annales Henri Poincare</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00023-005-0205-0\">https://doi.org/10.1007/s00023-005-0205-0</a>","chicago":"Erdös, László, David Hasler, and Jan Solovej. “Existence of the D0-D4 Bound State: A Detailed Proof.” <i>Annales Henri Poincare</i>. Birkhäuser, 2005. <a href=\"https://doi.org/10.1007/s00023-005-0205-0\">https://doi.org/10.1007/s00023-005-0205-0</a>.","mla":"Erdös, László, et al. “Existence of the D0-D4 Bound State: A Detailed Proof.” <i>Annales Henri Poincare</i>, vol. 6, no. 2, Birkhäuser, 2005, pp. 247–67, doi:<a href=\"https://doi.org/10.1007/s00023-005-0205-0\">10.1007/s00023-005-0205-0</a>.","ama":"Erdös L, Hasler D, Solovej J. Existence of the D0-D4 bound state: A detailed proof. <i>Annales Henri Poincare</i>. 2005;6(2):247-267. doi:<a href=\"https://doi.org/10.1007/s00023-005-0205-0\">10.1007/s00023-005-0205-0</a>"},"type":"journal_article","arxiv":1,"article_type":"original","day":"01","date_created":"2018-12-11T11:59:22Z","doi":"10.1007/s00023-005-0205-0","extern":"1","abstract":[{"text":"We consider the supersymmetric quantum mechanical system which is obtained by dimensionally reducing d = 6, N = 1 supersymmetric gauge theory with gauge group U(1) and a single charged hypermultiplet. Using the deformation method and ideas introduced by Porrati and Rozenberg [1], we present a detailed proof of the existence of a normalizable ground state for this system.","lang":"eng"}],"article_processing_charge":"No","page":"247 - 267","author":[{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Hasler, David","first_name":"David","last_name":"Hasler"},{"full_name":"Solovej, Jan","first_name":"Jan","last_name":"Solovej"}],"issue":"2","_id":"2743","external_id":{"arxiv":["abs/math-ph/0407020"]},"language":[{"iso":"eng"}],"intvolume":"         6","publist_id":"4149","date_updated":"2026-07-29T12:20:02Z","volume":6,"year":"2005","month":"04","publisher":"Birkhäuser","fulldoi":"https://doi.org/10.1007/s00023-005-0205-0"},{"OA_type":"green","OA_place":"repository","status":"public","publication":"Annales Henri Poincare","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"title":"Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field","oa_version":"None","date_published":"2004-08-01T00:00:00Z","arxiv":1,"article_type":"original","date_created":"2018-12-11T11:59:21Z","day":"01","type":"journal_article","citation":{"apa":"Erdös, L., &#38; Solovej, J. (2004). Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field. <i>Annales Henri Poincare</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00023-004-0180-x\">https://doi.org/10.1007/s00023-004-0180-x</a>","short":"L. Erdös, J. Solovej, Annales Henri Poincare 5 (2004) 671–741.","ista":"Erdös L, Solovej J. 2004. Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field. Annales Henri Poincare. 5(4), 671–741.","ieee":"L. Erdös and J. Solovej, “Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field,” <i>Annales Henri Poincare</i>, vol. 5, no. 4. Birkhäuser, pp. 671–741, 2004.","ama":"Erdös L, Solovej J. Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field. <i>Annales Henri Poincare</i>. 2004;5(4):671-741. doi:<a href=\"https://doi.org/10.1007/s00023-004-0180-x\">10.1007/s00023-004-0180-x</a>","mla":"Erdös, László, and Jan Solovej. “Uniform Lieb-Thirring Inequality for the Three-Dimensional Pauli Operator with a Strong Non-Homogeneous Magnetic Field.” <i>Annales Henri Poincare</i>, vol. 5, no. 4, Birkhäuser, 2004, pp. 671–741, doi:<a href=\"https://doi.org/10.1007/s00023-004-0180-x\">10.1007/s00023-004-0180-x</a>.","chicago":"Erdös, László, and Jan Solovej. “Uniform Lieb-Thirring Inequality for the Three-Dimensional Pauli Operator with a Strong Non-Homogeneous Magnetic Field.” <i>Annales Henri Poincare</i>. Birkhäuser, 2004. <a href=\"https://doi.org/10.1007/s00023-004-0180-x\">https://doi.org/10.1007/s00023-004-0180-x</a>."},"external_id":{"arxiv":["0304017"]},"language":[{"iso":"eng"}],"intvolume":"         5","publist_id":"4151","issue":"4","_id":"2741","page":"671 - 741","author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Solovej, Jan","first_name":"Jan","last_name":"Solovej"}],"extern":"1","doi":"10.1007/s00023-004-0180-x","abstract":[{"lang":"eng","text":"The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 1/2 in a magnetic field and an external potential. A new Lieb-Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic operators; (ii) a geometric construction of a Dirac operator with a constant magnetic field that approximates the original Dirac operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength."}],"article_processing_charge":"No","volume":5,"publisher":"Birkhäuser","month":"08","year":"2004","fulldoi":"https://doi.org/10.1007/s00023-004-0180-x","date_updated":"2026-09-22T13:07:17Z"}]