--- _id: '9318' abstract: - lang: eng text: We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. 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. 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). article_number: e28 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lea full_name: Bossmann, Lea id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425 last_name: Bossmann orcid: 0000-0002-6854-1343 - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.22 apa: Bossmann, L., Petrat, S. P., & Seiringer, R. (2021). Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.22 chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.22. ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy excitations for weakly interacting bosons,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021. ista: Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28. mla: Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics, Sigma, vol. 9, e28, Cambridge University Press, 2021, doi:10.1017/fms.2021.22. short: L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021). date_created: 2021-04-11T22:01:15Z date_published: 2021-03-26T00:00:00Z date_updated: 2023-08-07T14:35:06Z day: '26' ddc: - '510' department: - _id: RoSe doi: 10.1017/fms.2021.22 ec_funded: 1 external_id: isi: - '000634006900001' file: - access_level: open_access checksum: 17a3e6786d1e930cf0c14a880a6d7e92 content_type: application/pdf creator: dernst date_created: 2021-04-12T07:15:58Z date_updated: 2021-04-12T07:15:58Z file_id: '9319' file_name: 2021_ForumMath_Bossmann.pdf file_size: 883851 relation: main_file success: 1 file_date_updated: 2021-04-12T07:15:58Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 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 publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Asymptotic expansion of low-energy excitations for weakly interacting bosons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ... --- _id: '9550' abstract: - lang: eng 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. ' acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. 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 article_number: e44 article_processing_charge: No article_type: original author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38 apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.38 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.38. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021. ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44. mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38. short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021). date_created: 2021-06-13T22:01:33Z date_published: 2021-05-27T00:00:00Z date_updated: 2023-08-08T14:03:40Z day: '27' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2021.38 ec_funded: 1 external_id: arxiv: - '2008.07061' isi: - '000654960800001' file: - access_level: open_access checksum: 47c986578de132200d41e6d391905519 content_type: application/pdf creator: cziletti date_created: 2021-06-15T14:40:45Z date_updated: 2021-06-15T14:40:45Z file_id: '9555' file_name: 2021_ForumMath_Bao.pdf file_size: 483458 relation: main_file success: 1 file_date_updated: 2021-06-15T14:40:45Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Equipartition principle for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ... --- _id: '7790' abstract: - lang: eng 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 \U0001D70C and inverse temperature \U0001D6FD differs from the one of the noninteracting system by the correction term \U0001D70B\U0001D70C\U0001D70C\U0001D6FD\U0001D6FD . Here, is the scattering length of the interaction potential, and \U0001D6FD is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit \U0001D70C and if \U0001D6FD\U0001D70C ." article_number: e20 article_processing_charge: No article_type: original author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Simon full_name: Mayer, Simon id: 30C4630A-F248-11E8-B48F-1D18A9856A87 last_name: Mayer - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.17 apa: Deuchert, A., Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2020.17 chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics, Sigma. Cambridge University Press, 2020. https://doi.org/10.1017/fms.2020.17. ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” Forum of Mathematics, Sigma, 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. mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics, Sigma, vol. 8, e20, Cambridge University Press, 2020, doi:10.1017/fms.2020.17. short: A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020). date_created: 2020-05-03T22:00:48Z date_published: 2020-03-14T00:00:00Z date_updated: 2023-08-21T06:18:49Z day: '14' ddc: - '510' department: - _id: RoSe doi: 10.1017/fms.2020.17 ec_funded: 1 external_id: arxiv: - '1910.03372' isi: - '000527342000001' file: - access_level: open_access checksum: 8a64da99d107686997876d7cad8cfe1e content_type: application/pdf creator: dernst date_created: 2020-05-04T12:02:41Z date_updated: 2020-07-14T12:48:03Z file_id: '7797' file_name: 2020_ForumMath_Deuchert.pdf file_size: 692530 relation: main_file file_date_updated: 2020-07-14T12:48:03Z has_accepted_license: '1' intvolume: ' 8' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '7524' relation: earlier_version status: public scopus_import: '1' status: public title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 8 year: '2020' ... --- _id: '6182' 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." article_number: e8 article_processing_charge: No article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2 apa: Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2 chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2. ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, 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.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2. short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019). date_created: 2019-03-28T09:05:23Z date_published: 2019-03-26T00:00:00Z date_updated: 2023-09-07T12:54:12Z day: '26' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2019.2 ec_funded: 1 external_id: arxiv: - '1705.10661' isi: - '000488847100001' file: - access_level: open_access checksum: 933a472568221c73b2c3ce8c87bf6d15 content_type: application/pdf creator: dernst date_created: 2019-09-17T14:24:13Z date_updated: 2020-07-14T12:47:22Z file_id: '6883' file_name: 2019_Forum_Erdoes.pdf file_size: 1520344 relation: main_file file_date_updated: 2020-07-14T12:47:22Z has_accepted_license: '1' intvolume: ' 7' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '6179' relation: dissertation_contains status: public scopus_import: '1' status: public title: Random matrices with slow correlation decay tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 7 year: '2019' ...