[{"isi":1,"publisher":"Cambridge University Press","status":"public","intvolume":"         9","quality_controlled":"1","department":[{"_id":"RoSe"}],"publication":"Forum of Mathematics, Sigma","date_created":"2021-04-11T22:01:15Z","month":"03","acknowledgement":"The first author gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement No. 754411. The third author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"doi":"10.1017/fms.2021.22","ddc":["510"],"language":[{"iso":"eng"}],"title":"Asymptotic expansion of low-energy excitations for weakly interacting bosons","ec_funded":1,"citation":{"ama":"Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>","apa":"Bossmann, L., Petrat, S. P., &#38; Seiringer, R. (2021). Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","mla":"Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e28, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>.","chicago":"Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>.","ista":"Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28.","ieee":"L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy excitations for weakly interacting bosons,” <i>Forum of Mathematics, Sigma</i>, vol. 9. 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We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N."}],"file":[{"date_updated":"2021-04-12T07:15:58Z","access_level":"open_access","checksum":"17a3e6786d1e930cf0c14a880a6d7e92","file_name":"2021_ForumMath_Bossmann.pdf","file_size":883851,"creator":"dernst","success":1,"date_created":"2021-04-12T07:15:58Z","content_type":"application/pdf","relation":"main_file","file_id":"9319"}],"article_number":"e28","publication_identifier":{"eissn":["20505094"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-07T14:35:06Z","external_id":{"isi":["000634006900001"]},"scopus_import":"1","oa_version":"Published Version","has_accepted_license":"1","year":"2021","article_type":"original"},{"arxiv":1,"article_processing_charge":"No","file":[{"date_created":"2021-06-15T14:40:45Z","success":1,"file_id":"9555","relation":"main_file","content_type":"application/pdf","checksum":"47c986578de132200d41e6d391905519","access_level":"open_access","date_updated":"2021-06-15T14:40:45Z","file_size":483458,"creator":"cziletti","file_name":"2021_ForumMath_Bao.pdf"}],"article_number":"e44","date_published":"2021-05-27T00:00:00Z","_id":"9550","abstract":[{"text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. ","lang":"eng"}],"publication_status":"published","oa":1,"file_date_updated":"2021-06-15T14:40:45Z","volume":9,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_type":"original","oa_version":"Published Version","has_accepted_license":"1","year":"2021","date_updated":"2023-08-08T14:03:40Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"scopus_import":"1","publication_identifier":{"eissn":["20505094"]},"month":"05","date_created":"2021-06-13T22:01:33Z","publisher":"Cambridge University Press","isi":1,"department":[{"_id":"LaEr"}],"quality_controlled":"1","publication":"Forum of Mathematics, Sigma","status":"public","intvolume":"         9","ec_funded":1,"citation":{"apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 9. 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The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"ddc":["510"],"doi":"10.1017/fms.2021.38"},{"publication_status":"published","oa":1,"file_date_updated":"2020-07-14T12:48:03Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":8,"arxiv":1,"article_processing_charge":"No","file":[{"checksum":"8a64da99d107686997876d7cad8cfe1e","access_level":"open_access","date_updated":"2020-07-14T12:48:03Z","file_size":692530,"creator":"dernst","file_name":"2020_ForumMath_Deuchert.pdf","date_created":"2020-05-04T12:02:41Z","file_id":"7797","relation":"main_file","content_type":"application/pdf"}],"article_number":"e20","abstract":[{"text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 .","lang":"eng"}],"_id":"7790","date_published":"2020-03-14T00:00:00Z","external_id":{"isi":["000527342000001"],"arxiv":["1910.03372"]},"scopus_import":"1","date_updated":"2023-08-21T06:18:49Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["20505094"]},"article_type":"original","year":"2020","oa_version":"Published Version","has_accepted_license":"1","publisher":"Cambridge University Press","isi":1,"publication":"Forum of Mathematics, Sigma","quality_controlled":"1","department":[{"_id":"RoSe"}],"intvolume":"         8","status":"public","month":"03","date_created":"2020-05-03T22:00:48Z","related_material":{"record":[{"relation":"earlier_version","id":"7524","status":"public"}]},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"language":[{"iso":"eng"}],"doi":"10.1017/fms.2020.17","ddc":["510"],"citation":{"short":"A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020.","ista":"Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>."},"ec_funded":1,"title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","day":"14","author":[{"full_name":"Deuchert, Andreas","first_name":"Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746"},{"id":"30C4630A-F248-11E8-B48F-1D18A9856A87","first_name":"Simon","full_name":"Mayer, Simon","last_name":"Mayer"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"type":"journal_article"},{"publication_identifier":{"eissn":["20505094"]},"external_id":{"isi":["000488847100001"],"arxiv":["1705.10661"]},"scopus_import":"1","date_updated":"2023-09-07T12:54:12Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","has_accepted_license":"1","year":"2019","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":7,"file_date_updated":"2020-07-14T12:47:22Z","oa":1,"publication_status":"published","_id":"6182","date_published":"2019-03-26T00:00:00Z","abstract":[{"lang":"eng","text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."}],"file":[{"file_size":1520344,"creator":"dernst","file_name":"2019_Forum_Erdoes.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:22Z","checksum":"933a472568221c73b2c3ce8c87bf6d15","relation":"main_file","file_id":"6883","content_type":"application/pdf","date_created":"2019-09-17T14:24:13Z"}],"article_number":"e8","article_processing_charge":"No","arxiv":1,"doi":"10.1017/fms.2019.2","ddc":["510"],"language":[{"iso":"eng"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"type":"journal_article","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"day":"26","title":"Random matrices with slow correlation decay","citation":{"chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2019. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press, 2019.","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>"},"ec_funded":1,"status":"public","intvolume":"         7","publication":"Forum of Mathematics, Sigma","quality_controlled":"1","department":[{"_id":"LaEr"}],"isi":1,"publisher":"Cambridge University Press","date_created":"2019-03-28T09:05:23Z","month":"03"}]