[{"volume":5,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_updated":"2024-01-23T12:55:12Z","citation":{"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>.","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.","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>","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>","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>.","short":"D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008."},"year":"2023","date_published":"2023-12-15T00:00:00Z","type":"journal_article","doi":"10.2140/paa.2023.5.973","day":"15","publication_identifier":{"issn":["2578-5885","2578-5893"]},"abstract":[{"lang":"eng","text":"\r\nAbstract\r\nWe 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."}],"page":"973-1008","quality_controlled":"1","language":[{"iso":"eng"}],"keyword":["General Medicine"],"publisher":"Mathematical Sciences Publishers","article_type":"original","publication":"Pure and Applied Analysis","_id":"14854","author":[{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","last_name":"Mitrouskas"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"issue":"4","publication_status":"published","oa_version":"None","article_processing_charge":"No","department":[{"_id":"RoSe"}],"date_created":"2024-01-22T08:24:23Z","month":"12","title":"Ubiquity of bound states for the strongly coupled polaron","intvolume":"         5"},{"acknowledgement":"Financial support by the European Union’s Horizon 2020 research and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No. 754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227 (N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.), the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel Griesemer for helpful discussions.","volume":3,"doi":"10.2140/paa.2021.3.653","arxiv":1,"day":"01","abstract":[{"lang":"eng","text":"We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2."}],"date_updated":"2024-02-05T10:02:45Z","year":"2021","citation":{"apa":"Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>","ama":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. <i>Pure and Applied Analysis</i>. 2021;3(4):653-676. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>","chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.653\">https://doi.org/10.2140/paa.2021.3.653</a>.","ieee":"N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 653–676, 2021.","mla":"Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.653\">10.2140/paa.2021.3.653</a>.","short":"N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer, Pure and Applied Analysis 3 (2021) 653–676.","ista":"Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 3(4), 653–676."},"external_id":{"arxiv":["2005.02098"]},"publisher":"Mathematical Sciences Publishers","article_type":"original","page":"653-676","quality_controlled":"1","ec_funded":1,"publication_status":"published","article_processing_charge":"No","date_created":"2024-01-28T23:01:43Z","department":[{"_id":"RoSe"}],"title":"Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron","intvolume":"         3","_id":"14889","scopus_import":"1","author":[{"last_name":"Leopold","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","first_name":"David Johannes","last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes"},{"orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira","first_name":"Simone Anna Elvira","last_name":"Rademacher","id":"856966FE-A408-11E9-977E-802DE6697425"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"issue":"4","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2005.02098","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"oa":1,"date_published":"2021-10-01T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"oa_version":"Preprint","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"month":"10","publication":"Pure and Applied Analysis"},{"volume":3,"acknowledgement":"We are grateful for the hospitality of Central China Normal University (CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher, Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research\r\nTraining Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk lodowska-Curie Grant Agreement No. 754411.","year":"2021","citation":{"ista":"Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726.","mla":"Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>.","short":"L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis 3 (2021) 677–726.","chicago":"Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov Dynamics.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/paa.2021.3.677\">https://doi.org/10.2140/paa.2021.3.677</a>.","ieee":"L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,” <i>Pure and Applied Analysis</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 677–726, 2021.","apa":"Bossmann, L., Petrat, S. P., Pickl, P., &#38; Soffer, A. (2021). Beyond Bogoliubov dynamics. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2021.3.677\">https://doi.org/10.2140/paa.2021.3.677</a>","ama":"Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. <i>Pure and Applied Analysis</i>. 2021;3(4):677-726. doi:<a href=\"https://doi.org/10.2140/paa.2021.3.677\">10.2140/paa.2021.3.677</a>"},"date_updated":"2024-02-05T09:26:31Z","external_id":{"arxiv":["1912.11004"]},"day":"01","doi":"10.2140/paa.2021.3.677","arxiv":1,"abstract":[{"lang":"eng","text":"We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions."}],"quality_controlled":"1","ec_funded":1,"page":"677-726","publisher":"Mathematical Sciences Publishers","article_type":"original","scopus_import":"1","_id":"14890","issue":"4","author":[{"full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"},{"full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","last_name":"Petrat","first_name":"Sören P","id":"40AC02DC-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pickl","first_name":"Peter","full_name":"Pickl, Peter"},{"last_name":"Soffer","first_name":"Avy","full_name":"Soffer, Avy"}],"article_processing_charge":"No","department":[{"_id":"RoSe"}],"date_created":"2024-01-28T23:01:43Z","publication_status":"published","intvolume":"         3","title":"Beyond Bogoliubov dynamics","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.11004","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","date_published":"2021-10-01T00:00:00Z","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"oa":1,"language":[{"iso":"eng"}],"publication":"Pure and Applied Analysis","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Preprint","month":"10"},{"publication_status":"published","date_created":"2024-01-28T23:01:44Z","department":[{"_id":"RoSe"}],"article_processing_charge":"No","title":" The local density approximation in density functional theory","intvolume":"         2","_id":"14891","scopus_import":"1","author":[{"last_name":"Lewin","first_name":"Mathieu","full_name":"Lewin, Mathieu"},{"first_name":"Elliott H.","last_name":"Lieb","full_name":"Lieb, Elliott H."},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"issue":"1","publisher":"Mathematical Sciences Publishers","article_type":"original","page":"35-73","quality_controlled":"1","doi":"10.2140/paa.2020.2.35","arxiv":1,"day":"01","abstract":[{"text":"We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space.","lang":"eng"}],"date_updated":"2024-01-29T09:01:12Z","year":"2020","citation":{"ista":"Lewin M, Lieb EH, Seiringer R. 2020.  The local density approximation in density functional theory. Pure and Applied Analysis. 2(1), 35–73.","short":"M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73.","mla":"Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>, vol. 2, no. 1, Mathematical Sciences Publishers, 2020, pp. 35–73, doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>.","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density Approximation in Density Functional Theory.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>.","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation in density functional theory,” <i>Pure and Applied Analysis</i>, vol. 2, no. 1. Mathematical Sciences Publishers, pp. 35–73, 2020.","ama":"Lewin M, Lieb EH, Seiringer R.  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. 2020;2(1):35-73. doi:<a href=\"https://doi.org/10.2140/paa.2020.2.35\">10.2140/paa.2020.2.35</a>","apa":"Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2020).  The local density approximation in density functional theory. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2020.2.35\">https://doi.org/10.2140/paa.2020.2.35</a>"},"external_id":{"arxiv":["1903.04046"]},"volume":2,"oa_version":"Preprint","month":"01","publication":"Pure and Applied Analysis","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"oa":1,"date_published":"2020-01-01T00:00:00Z","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1903.04046"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"issue":"4","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"_id":"6186","intvolume":"         1","title":"Cusp universality for random matrices, II: The real symmetric case","department":[{"_id":"LaEr"}],"date_created":"2019-03-28T10:21:17Z","article_processing_charge":"No","publication_status":"published","ec_funded":1,"quality_controlled":"1","page":"615–707","article_type":"original","publisher":"MSP","external_id":{"arxiv":["1811.04055"]},"year":"2019","citation":{"mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>, vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis  1 (2019) 615–707.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. MSP. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. 2019;1(4):615–707. doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” <i>Pure and Applied Analysis </i>, vol. 1, no. 4. MSP, pp. 615–707, 2019.","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>. MSP, 2019. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>."},"date_updated":"2023-09-07T12:54:12Z","abstract":[{"lang":"eng","text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion."}],"day":"12","arxiv":1,"doi":"10.2140/paa.2019.1.615","volume":1,"publication":"Pure and Applied Analysis ","month":"10","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2019-10-12T00:00:00Z","oa":1,"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}]}]