--- _id: '11783' abstract: - lang: eng text: We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix. acknowledgement: "The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged." article_number: '061102' 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 citation: ama: Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 2022;63(6). doi:10.1063/5.0089983 apa: Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0089983 chicago: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0089983. ieee: L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose gas,” Journal of Mathematical Physics, vol. 63, no. 6. AIP Publishing, 2022. ista: Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102. mla: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics, vol. 63, no. 6, 061102, AIP Publishing, 2022, doi:10.1063/5.0089983. short: L. Bossmann, Journal of Mathematical Physics 63 (2022). date_created: 2022-08-11T06:37:52Z date_published: 2022-06-10T00:00:00Z date_updated: 2023-08-03T12:46:28Z day: '10' ddc: - '530' department: - _id: RoSe doi: 10.1063/5.0089983 ec_funded: 1 external_id: arxiv: - '2203.00730' isi: - '000809648100002' file: - access_level: open_access checksum: d0d32c338c1896680174be88c70968fa content_type: application/pdf creator: dernst date_created: 2022-08-11T07:03:02Z date_updated: 2022-08-11T07:03:02Z file_id: '11784' file_name: 2022_JourMathPhysics_Bossmann.pdf file_size: 5957888 relation: main_file success: 1 file_date_updated: 2022-08-11T07:03:02Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '6' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Low-energy spectrum and dynamics of the weakly interacting Bose gas 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: 63 year: '2022' ... --- _id: '11917' abstract: - lang: eng text: We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to more general interactions. Furthermore, we derive a new lower bound which agrees with the upper bound in leading order. acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding provided by IST Austria." article_number: '9' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4 apa: Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02940-4 chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4. ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly interacting bosons,” Journal of Statistical Physics, vol. 188. Springer Nature, 2022. ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 188, 9. mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188, 9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4. short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022). date_created: 2022-08-18T07:23:26Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-08-03T12:55:58Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s10955-022-02940-4 ec_funded: 1 external_id: isi: - '000805175000001' file: - access_level: open_access checksum: 44418cb44f07fa21ed3907f85abf7f39 content_type: application/pdf creator: dernst date_created: 2022-08-18T08:09:00Z date_updated: 2022-08-18T08:09:00Z file_id: '11922' file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf file_size: 483481 relation: main_file success: 1 file_date_updated: 2022-08-18T08:09:00Z has_accepted_license: '1' intvolume: ' 188' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' 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 - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Large deviation estimates 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: 188 year: '2022' ... --- _id: '12083' abstract: - lang: eng text: We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both a law of large numbers and a central limit theorem. acknowledgement: S.R. would like to thank Robert Seiringer and Benedikt Stufler for helpful discussions. Funding from the European Union’s Horizon 2020 Research and Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged. article_number: '081902' article_processing_charge: No article_type: original author: - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 citation: ama: Rademacher SAE. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 2022;63(8). doi:10.1063/5.0086712 apa: Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0086712 chicago: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0086712. ieee: S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” Journal of Mathematical Physics, vol. 63, no. 8. AIP Publishing, 2022. ista: Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 63(8), 081902. mla: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” Journal of Mathematical Physics, vol. 63, no. 8, 081902, AIP Publishing, 2022, doi:10.1063/5.0086712. short: S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022). date_created: 2022-09-11T22:01:56Z date_published: 2022-08-25T00:00:00Z date_updated: 2023-08-03T13:57:19Z day: '25' ddc: - '510' department: - _id: RoSe doi: 10.1063/5.0086712 ec_funded: 1 external_id: arxiv: - '2112.04817' isi: - '000844402500001' file: - access_level: open_access checksum: e6fb0cf3f0327739c5e69a2cfc4020eb content_type: application/pdf creator: dernst date_created: 2022-09-12T07:35:34Z date_updated: 2022-09-12T07:35:34Z file_id: '12089' file_name: 2022_JourMathPhysics_Rademacher.pdf file_size: 4552261 relation: main_file success: 1 file_date_updated: 2022-09-12T07:35:34Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '8' language: - iso: eng month: '08' 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 - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Mathematical Physics publication_identifier: issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Dependent random variables in quantum dynamics 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: 63 year: '2022' ... --- _id: '12390' abstract: - lang: eng 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" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 citation: ama: Brooks M. Translation-invariant quantum systems with effectively broken symmetry. 2022. doi:10.15479/at:ista:12390 apa: Brooks, M. (2022). Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:12390 chicago: Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively Broken Symmetry.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:12390. ieee: 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. mla: Brooks, Morris. Translation-Invariant Quantum Systems with Effectively Broken Symmetry. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12390. short: M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken Symmetry, Institute of Science and Technology Austria, 2022. date_created: 2023-01-26T10:00:42Z date_published: 2022-12-15T00:00:00Z date_updated: 2023-08-07T13:32:09Z day: '15' ddc: - '500' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:12390 ec_funded: 1 file: - access_level: open_access checksum: b31460e937f33b557abb40ebef02b567 content_type: application/pdf creator: cchlebak date_created: 2023-01-26T10:02:34Z date_updated: 2023-01-26T10:02:34Z file_id: '12391' file_name: Brooks_Thesis.pdf file_size: 3095225 relation: main_file success: 1 - access_level: closed checksum: 9751869fa5e7981588ad4228f4fd4bd6 content_type: application/octet-stream creator: cchlebak date_created: 2023-01-26T10:02:42Z date_updated: 2023-01-26T10:02:42Z file_id: '12392' file_name: Brooks_Thesis.tex file_size: 809842 relation: source_file file_date_updated: 2023-01-26T10:02:42Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: '196' project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '9005' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Translation-invariant quantum systems with effectively broken symmetry tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '11732' abstract: - lang: eng text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)" article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9 apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9 chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9. ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022. ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5. mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9. short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022). date_created: 2022-08-05T11:36:56Z date_published: 2022-07-29T00:00:00Z date_updated: 2023-09-05T14:57:49Z day: '29' ddc: - '530' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1007/s10955-022-02965-9 ec_funded: 1 external_id: isi: - '000833007200002' file: - access_level: open_access checksum: b398c4dbf65f71d417981d6e366427e9 content_type: application/pdf creator: dernst date_created: 2022-08-08T07:36:34Z date_updated: 2022-08-08T07:36:34Z file_id: '11746' file_name: 2022_JourStatisticalPhysics_Henheik.pdf file_size: 419563 relation: main_file success: 1 file_date_updated: 2022-08-08T07:36:34Z has_accepted_license: '1' intvolume: ' 189' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS energy gap at high density 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: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 189 year: '2022' ...