[{"citation":{"chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” *Journal of Mathematical Physics*. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. *Journal of Mathematical Physics*. AIP Publishing. https://doi.org/10.1063/5.0051632","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. *Journal of Mathematical Physics*. 2022;63(1). doi:10.1063/5.0051632","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” *Journal of Mathematical Physics*, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” *Journal of Mathematical Physics*, vol. 63, no. 1. AIP Publishing, 2022.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022)."},"volume":63,"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","external_id":{"arxiv":["2012.15238"]},"date_published":"2022-01-03T00:00:00Z","month":"01","article_type":"original","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","publisher":"AIP Publishing","author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"status":"public","oa":1,"language":[{"iso":"eng"}],"article_number":"011901","day":"03","issue":"1","oa_version":"Preprint","article_processing_charge":"No","publication":"Journal of Mathematical Physics","date_updated":"2022-04-04T06:19:24Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-01-03T12:19:48Z","keyword":["mathematical physics","statistical and nonlinear physics"],"doi":"10.1063/5.0051632","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 63","publication_status":"published","ec_funded":1,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"type":"journal_article","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}],"year":"2022","abstract":[{"lang":"eng","text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article."}],"_id":"10600"},{"status":"public","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"}],"has_accepted_license":"1","acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","publisher":"Springer Nature","date_published":"2022-01-11T00:00:00Z","month":"01","external_id":{"arxiv":["2106.02015"]},"article_type":"original","file_date_updated":"2022-01-14T07:27:45Z","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"volume":25,"title":" The BCS critical temperature at high density","citation":{"ieee":"S. J. Henheik, “ The BCS critical temperature at high density,” *Mathematical Physics, Analysis and Geometry*, vol. 25, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","ama":"Henheik SJ. The BCS critical temperature at high density. *Mathematical Physics, Analysis and Geometry*. 2022;25(1). doi:10.1007/s11040-021-09415-0","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","mla":"Henheik, Sven Joscha. “ The BCS Critical Temperature at High Density.” *Mathematical Physics, Analysis and Geometry*, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0.","chicago":"Henheik, Sven Joscha. “ The BCS Critical Temperature at High Density.” *Mathematical Physics, Analysis and Geometry*. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. *Mathematical Physics, Analysis and Geometry*. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0"},"scopus_import":"1","date_created":"2022-01-13T15:40:53Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ddc":["514"],"doi":"10.1007/s11040-021-09415-0","keyword":["geometry and topology","mathematical physics"],"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","date_updated":"2022-04-05T14:08:23Z","publication":"Mathematical Physics, Analysis and Geometry","issue":"1","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"day":"11","language":[{"iso":"eng"}],"article_number":"3","publication_status":"published","intvolume":" 25","ec_funded":1,"user_id":"4A997E50-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","type":"journal_article","_id":"10623","year":"2022","abstract":[{"lang":"eng","text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory."}],"license":"https://creativecommons.org/licenses/by/4.0/","file":[{"date_updated":"2022-01-14T07:27:45Z","file_size":505804,"file_name":"2022_MathPhyAnalGeo_Henheik.pdf","content_type":"application/pdf","access_level":"open_access","date_created":"2022-01-14T07:27:45Z","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","success":1,"file_id":"10624","creator":"cchlebak","relation":"main_file"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}]},{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","ec_funded":1,"intvolume":" 112","publication_status":"published","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"file":[{"access_level":"open_access","content_type":"application/pdf","date_created":"2022-01-19T09:41:14Z","checksum":"7e8e69b76e892c305071a4736131fe18","date_updated":"2022-01-19T09:41:14Z","file_size":357547,"file_name":"2022_LettersMathPhys_Henheik.pdf","creator":"cchlebak","relation":"main_file","success":1,"file_id":"10647"}],"year":"2022","abstract":[{"lang":"eng","text":"Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences."}],"_id":"10642","type":"journal_article","quality_controlled":"1","volume":112,"citation":{"mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” *Letters in Mathematical Physics*, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y.","ista":"Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9.","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. *Letters in Mathematical Physics*. 2022;112(1). doi:10.1007/s11005-021-01494-y","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” *Letters in Mathematical Physics*, vol. 112, no. 1. Springer Nature, 2022.","apa":"Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. *Letters in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y","chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” *Letters in Mathematical Physics*. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y."},"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"file_date_updated":"2022-01-19T09:41:14Z","article_type":"original","external_id":{"arxiv":["2106.13780"]},"date_published":"2022-01-18T00:00:00Z","month":"01","acknowledgement":"J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL.","publisher":"Springer Nature","has_accepted_license":"1","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"full_name":"Teufel, Stefan","first_name":"Stefan","last_name":"Teufel"},{"full_name":"Wessel, Tom","first_name":"Tom","last_name":"Wessel"}],"status":"public","article_number":"9","language":[{"iso":"eng"}],"day":"18","oa":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"issue":"1","date_updated":"2022-01-24T07:55:43Z","publication":"Letters in Mathematical Physics","oa_version":"Published Version","article_processing_charge":"Yes","keyword":["mathematical physics","statistical and nonlinear physics"],"doi":"10.1007/s11005-021-01494-y","ddc":["530"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-01-18T16:18:25Z"},{"day":"18","language":[{"iso":"eng"}],"article_number":"e4","oa":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_updated":"2022-01-19T09:31:10Z","publication":"Forum of Mathematics, Sigma","article_processing_charge":"Yes","oa_version":"Published Version","doi":"10.1017/fms.2021.80","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"date_created":"2022-01-18T16:18:51Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ddc":["510"],"volume":10,"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. *Forum of Mathematics, Sigma*. 2022;10. doi:10.1017/fms.2021.80","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” *Forum of Mathematics, Sigma*, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” *Forum of Mathematics, Sigma*, vol. 10. Cambridge University Press, 2022.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” *Forum of Mathematics, Sigma*. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. *Forum of Mathematics, Sigma*. Cambridge University Press. https://doi.org/10.1017/fms.2021.80"},"publication_identifier":{"eissn":["2050-5094"]},"external_id":{"arxiv":["2012.15239"]},"month":"01","date_published":"2022-01-18T00:00:00Z","article_type":"original","file_date_updated":"2022-01-19T09:27:43Z","publisher":"Cambridge University Press","acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","has_accepted_license":"1","status":"public","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"file":[{"content_type":"application/pdf","access_level":"open_access","checksum":"87592a755adcef22ea590a99dc728dd3","date_created":"2022-01-19T09:27:43Z","date_updated":"2022-01-19T09:27:43Z","file_size":705323,"file_name":"2022_ForumMathSigma_Henheik.pdf","relation":"main_file","creator":"cchlebak","success":1,"file_id":"10646"}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"_id":"10643","year":"2022","abstract":[{"text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n","lang":"eng"}],"quality_controlled":"1","type":"journal_article","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","intvolume":" 10","publication_status":"published","ec_funded":1},{"citation":{"short":"R. Seiringer, Reviews in Mathematical Physics 33 (2021).","ieee":"R. Seiringer, “The polaron at strong coupling,” *Reviews in Mathematical Physics*, vol. 33, no. 01. World Scientific Publishing, 2021.","mla":"Seiringer, Robert. “The Polaron at Strong Coupling.” *Reviews in Mathematical Physics*, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120.","ama":"Seiringer R. The polaron at strong coupling. *Reviews in Mathematical Physics*. 2021;33(01). doi:10.1142/s0129055x20600120","ista":"Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012.","apa":"Seiringer, R. (2021). The polaron at strong coupling. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120","chicago":"Seiringer, Robert. “The Polaron at Strong Coupling.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120."},"scopus_import":"1","volume":33,"title":"The polaron at strong coupling","date_published":"2021-02-01T00:00:00Z","external_id":{"arxiv":["1912.12509"]},"article_type":"original","month":"02","publication_identifier":{"issn":["0129-055X","1793-6659"]},"acknowledgement":"This work was supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo. 694227).","publisher":"World Scientific Publishing","status":"public","author":[{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"day":"01","article_number":"2060012","language":[{"iso":"eng"}],"issue":"01","oa_version":"Preprint","article_processing_charge":"No","publication":"Reviews in Mathematical Physics","date_updated":"2022-03-18T08:19:49Z","date_created":"2022-03-18T08:11:34Z","department":[{"_id":"RoSe"}],"doi":"10.1142/s0129055x20600120","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"intvolume":" 33","publication_status":"published","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1912.12509","open_access":"1"}],"type":"journal_article","_id":"10852","year":"2021","abstract":[{"text":" We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.","lang":"eng"}]},{"oa":1,"day":"12","article_number":"20","language":[{"iso":"eng"}],"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","publication":"Letters in Mathematical Physics","date_updated":"2021-02-15T09:32:40Z","date_created":"2021-02-15T09:27:14Z","department":[{"_id":"GradSch"}],"ddc":["510"],"doi":"10.1007/s11005-021-01358-5","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"citation":{"ieee":"A. B. Lauritsen, “The BCS energy gap at low density,” *Letters in Mathematical Physics*, vol. 111. Springer Nature, 2021.","short":"A.B. Lauritsen, Letters in Mathematical Physics 111 (2021).","ama":"Lauritsen AB. The BCS energy gap at low density. *Letters in Mathematical Physics*. 2021;111. doi:10.1007/s11005-021-01358-5","ista":"Lauritsen AB. 2021. The BCS energy gap at low density. Letters in Mathematical Physics. 111, 20.","mla":"Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” *Letters in Mathematical Physics*, vol. 111, 20, Springer Nature, 2021, doi:10.1007/s11005-021-01358-5.","chicago":"Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” *Letters in Mathematical Physics*. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01358-5.","apa":"Lauritsen, A. B. (2021). The BCS energy gap at low density. *Letters in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s11005-021-01358-5"},"volume":111,"title":"The BCS energy gap at low density","month":"02","date_published":"2021-02-12T00:00:00Z","article_type":"original","file_date_updated":"2021-02-15T09:31:07Z","publication_identifier":{"issn":["0377-9017","1573-0530"]},"has_accepted_license":"1","acknowledgement":"Most of this work was done as part of the author’s master’s thesis. The author would like to thank Jan Philip Solovej for his supervision of this process.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria)","publisher":"Springer Nature","status":"public","author":[{"last_name":"Lauritsen","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"file":[{"file_name":"2021_LettersMathPhysics_Lauritsen.pdf","file_size":329332,"date_updated":"2021-02-15T09:31:07Z","checksum":"eaf1b3ff5026f120f0929a5c417dc842","date_created":"2021-02-15T09:31:07Z","access_level":"open_access","content_type":"application/pdf","file_id":"9122","success":1,"relation":"main_file","creator":"dernst"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","type":"journal_article","_id":"9121","year":"2021","abstract":[{"text":"We show that the energy gap for the BCS gap equation is\r\nΞ=μ(8e−2+o(1))exp(π2μ−−√a)\r\nin the low density limit μ→0. Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","intvolume":" 111"},{"publication_identifier":{"issn":["0129-055X","1793-6659"]},"external_id":{"arxiv":["2002.08669"]},"date_published":"2021-02-01T00:00:00Z","month":"02","article_type":"original","scopus_import":"1","title":"Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results","citation":{"short":"S.J. Henheik, S. Teufel, Reviews in Mathematical Physics 33 (2021).","ieee":"S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results,” *Reviews in Mathematical Physics*, vol. 33, no. 01. World Scientific Publishing, 2021.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” *Reviews in Mathematical Physics*, vol. 33, no. 01, 2060004, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600041.","ama":"Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. *Reviews in Mathematical Physics*. 2021;33(01). doi:10.1142/s0129055x20600041","ista":"Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 33(01), 2060004.","apa":"Henheik, S. J., & Teufel, S. (2021). Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600041","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600041."},"volume":33,"status":"public","author":[{"last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"extern":"1","publisher":"World Scientific Publishing","has_accepted_license":"1","issue":"01","day":"01","article_number":"2060004","language":[{"iso":"eng"}],"oa":1,"doi":"10.1142/s0129055x20600041","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2021-03-26T11:29:46Z","ddc":["500"],"date_updated":"2021-03-29T07:50:18Z","publication":"Reviews in Mathematical Physics","oa_version":"Preprint","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","intvolume":" 33","_id":"9285","year":"2021","abstract":[{"text":"We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.","lang":"eng"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.08669"}],"type":"journal_article"},{"publisher":"AIP","acknowledgement":"The author would like to thank Robert Seiringer for guidance and many helpful comments on this project. The author would also like to thank Mathieu Lewin for his comments on the manuscript and Lorenzo Portinale for providing his lecture notes for the course “Mathematics of quantum many-body systems” in spring 2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these lecture notes.","has_accepted_license":"1","status":"public","author":[{"orcid":"0000-0003-4476-2288","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"volume":62,"title":"Floating Wigner crystal and periodic jellium configurations","scopus_import":"1","citation":{"mla":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” *Journal of Mathematical Physics*, vol. 62, no. 8, 083305, AIP, 2021, doi:10.1063/5.0053494.","ista":"Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305.","ama":"Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. *Journal of Mathematical Physics*. 2021;62(8). doi:10.1063/5.0053494","short":"A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).","ieee":"A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” *Journal of Mathematical Physics*, vol. 62, no. 8. AIP, 2021.","apa":"Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. *Journal of Mathematical Physics*. AIP. https://doi.org/10.1063/5.0053494","chicago":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” *Journal of Mathematical Physics*. AIP, 2021. https://doi.org/10.1063/5.0053494."},"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"external_id":{"arxiv":["2103.07975"]},"date_published":"2021-08-01T00:00:00Z","month":"08","article_type":"original","file_date_updated":"2021-10-27T12:57:06Z","publication":"Journal of Mathematical Physics","date_updated":"2021-10-27T13:22:51Z","oa_version":"Published Version","article_processing_charge":"No","doi":"10.1063/5.0053494","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2021-08-12T07:08:36Z","ddc":["530"],"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"day":"01","language":[{"iso":"eng"}],"article_number":"083305","oa":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"issue":"8","intvolume":" 62","publication_status":"published","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9891","year":"2021","abstract":[{"lang":"eng","text":"Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron gas) with density equal to a characteristic function. This allows us to show that three definitions of the jellium energy coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache [“Equality of the Jellium and uniform electron gas next-order asymptotic terms for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized energy” studied in a series of papers by Serfaty and others, and thus, by the work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2-sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations."}],"quality_controlled":"1","type":"journal_article","file":[{"file_id":"10188","success":1,"creator":"cziletti","relation":"main_file","file_name":"2021_JMathPhy_Lauritsen.pdf","file_size":4352640,"date_updated":"2021-10-27T12:57:06Z","checksum":"d035be2b894c4d50d90ac5ce252e27cd","date_created":"2021-10-27T12:57:06Z","content_type":"application/pdf","access_level":"open_access"}]},{"day":"30","language":[{"iso":"eng"}],"oa":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication":"Communications in Mathematical Physics","date_updated":"2022-05-13T06:56:44Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00220-021-04199-4","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"date_created":"2021-08-30T10:07:44Z","department":[{"_id":"JaMa"}],"ddc":["621"],"page":"761–791","title":"Complete gradient estimates of quantum Markov semigroups","volume":387,"citation":{"chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” *Communications in Mathematical Physics*. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04199-4.","apa":"Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. *Communications in Mathematical Physics*. 2021;387:761–791. doi:10.1007/s00220-021-04199-4","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” *Communications in Mathematical Physics*, vol. 387, Springer Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” *Communications in Mathematical Physics*, vol. 387. Springer Nature, pp. 761–791, 2021.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791."},"scopus_import":"1","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"external_id":{"arxiv":["2007.13506"]},"article_type":"original","date_published":"2021-08-30T00:00:00Z","month":"08","file_date_updated":"2021-09-08T09:46:34Z","publisher":"Springer Nature","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","has_accepted_license":"1","status":"public","author":[{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth"},{"last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","first_name":"Haonan"}],"file":[{"access_level":"open_access","content_type":"application/pdf","date_created":"2021-09-08T07:34:24Z","checksum":"8a602f916b1c2b0dc1159708b7cb204b","date_updated":"2021-09-08T09:46:34Z","file_name":"2021_CommunMathPhys_Wirth.pdf","file_size":505971,"relation":"main_file","creator":"cchlebak","file_id":"9990"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"_id":"9973","year":"2021","abstract":[{"lang":"eng","text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors."}],"quality_controlled":"1","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"intvolume":" 387","publication_status":"published"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","intvolume":" 374","main_file_link":[{"url":"https://arxiv.org/abs/1809.08947","open_access":"1"}],"quality_controlled":"1","type":"journal_article","_id":"8415","year":"2019","abstract":[{"lang":"eng","text":"We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift on three symbols that provides a natural labeling of all periodic orbits. We study the following inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of periodic orbits together with their labeling), determine the geometry of the billiard table? We show that from the Marked Length Spectrum it is possible to recover the curvature at periodic points of period two, as well as the Lyapunov exponent of each periodic orbit."}],"page":"1531-1575","citation":{"ista":"Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 374(3), 1531–1575.","ama":"Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. *Communications in Mathematical Physics*. 2019;374(3):1531-1575. doi:10.1007/s00220-019-03448-x","mla":"Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” *Communications in Mathematical Physics*, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x.","ieee":"P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards,” *Communications in Mathematical Physics*, vol. 374, no. 3. Springer Nature, pp. 1531–1575, 2019.","short":"P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575.","chicago":"Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” *Communications in Mathematical Physics*. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03448-x.","apa":"Bálint, P., De Simoi, J., Kaloshin, V., & Leguil, M. (2019). Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-019-03448-x"},"volume":374,"title":"Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards","external_id":{"arxiv":["1809.08947"]},"article_type":"original","date_published":"2019-05-09T00:00:00Z","month":"05","publication_identifier":{"issn":["0010-3616","1432-0916"]},"publisher":"Springer Nature","status":"public","author":[{"first_name":"Péter","full_name":"Bálint, Péter","last_name":"Bálint"},{"first_name":"Jacopo","full_name":"De Simoi, Jacopo","last_name":"De Simoi"},{"last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Leguil","full_name":"Leguil, Martin","first_name":"Martin"}],"extern":"1","oa":1,"day":"09","language":[{"iso":"eng"}],"issue":"3","article_processing_charge":"No","oa_version":"Preprint","publication":"Communications in Mathematical Physics","date_updated":"2021-01-12T08:19:08Z","date_created":"2020-09-17T10:41:27Z","doi":"10.1007/s00220-019-03448-x","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"]},{"date_created":"2020-09-17T10:41:43Z","quality_controlled":"1","type":"journal_article","_id":"8417","doi":"10.1007/s00220-018-3248-z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"abstract":[{"text":"The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show the existence of orbits whose angular momentum performs arbitrary excursions in a large region. In particular, there exist diffusive orbits, that is, with a large variation of angular momentum. The leading idea of the proof consists in analyzing parabolic motions of the comet. By a well-known result of McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold at parabolic infinity. On P∞ it is possible to define two scattering maps, which contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic both in the future and the past. Since the inner dynamics inside P∞ is trivial, two different scattering maps are used. The combination of these two scattering maps permits the design of the desired diffusive pseudo-orbits. Using shadowing techniques and these pseudo orbits we show the existence of true trajectories of the RPETBP whose angular momentum varies in any predetermined fashion.","lang":"eng"}],"year":"2018","article_processing_charge":"No","oa_version":"None","publication":"Communications in Mathematical Physics","date_updated":"2021-01-12T08:19:08Z","issue":"3","day":"05","language":[{"iso":"eng"}],"status":"public","extern":"1","author":[{"first_name":"Amadeu","full_name":"Delshams, Amadeu","last_name":"Delshams"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","full_name":"Kaloshin, Vadim"},{"first_name":"Abraham","full_name":"de la Rosa, Abraham","last_name":"de la Rosa"},{"last_name":"Seara","first_name":"Tere M.","full_name":"Seara, Tere M."}],"publisher":"Springer Nature","publication_status":"published","intvolume":" 366","date_published":"2018-09-05T00:00:00Z","month":"09","article_type":"original","publication_identifier":{"issn":["0010-3616","1432-0916"]},"page":"1173-1228","title":"Global instability in the restricted planar elliptic three body problem","citation":{"ista":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 366(3), 1173–1228.","ama":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted planar elliptic three body problem. *Communications in Mathematical Physics*. 2018;366(3):1173-1228. doi:10.1007/s00220-018-3248-z","mla":"Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” *Communications in Mathematical Physics*, vol. 366, no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z.","ieee":"A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability in the restricted planar elliptic three body problem,” *Communications in Mathematical Physics*, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.","short":"A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical Physics 366 (2018) 1173–1228.","chicago":"Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” *Communications in Mathematical Physics*. Springer Nature, 2018. https://doi.org/10.1007/s00220-018-3248-z.","apa":"Delshams, A., Kaloshin, V., de la Rosa, A., & Seara, T. M. (2018). Global instability in the restricted planar elliptic three body problem. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-018-3248-z"},"volume":366,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"extern":"1","author":[{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Zhang","full_name":"Zhang, Ke","first_name":"Ke"}],"status":"public","publisher":"IOP Publishing","date_published":"2018-10-15T00:00:00Z","article_type":"original","month":"10","external_id":{"arxiv":["1706.07968"]},"publication_identifier":{"issn":["0951-7715","1361-6544"]},"title":"Density of convex billiards with rational caustics","citation":{"apa":"Kaloshin, V., & Zhang, K. (2018). Density of convex billiards with rational caustics. *Nonlinearity*. IOP Publishing. https://doi.org/10.1088/1361-6544/aadc12","chicago":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” *Nonlinearity*. IOP Publishing, 2018. https://doi.org/10.1088/1361-6544/aadc12.","mla":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” *Nonlinearity*, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12.","ama":"Kaloshin V, Zhang K. Density of convex billiards with rational caustics. *Nonlinearity*. 2018;31(11):5214-5234. doi:10.1088/1361-6544/aadc12","ista":"Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.","short":"V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.","ieee":"V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,” *Nonlinearity*, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018."},"volume":31,"page":"5214-5234","date_created":"2020-09-17T10:42:09Z","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"doi":"10.1088/1361-6544/aadc12","article_processing_charge":"No","oa_version":"Preprint","date_updated":"2021-01-12T08:19:10Z","publication":"Nonlinearity","issue":"11","oa":1,"language":[{"iso":"eng"}],"day":"15","intvolume":" 31","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1706.07968","open_access":"1"}],"quality_controlled":"1","abstract":[{"text":"We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number 1/q is polynomially sense in the smooth case, and exponentially dense in the analytic case.","lang":"eng"}],"year":"2018","_id":"8420"},{"language":[{"iso":"eng"}],"day":"30","issue":"8","publication":"Nonlinearity","date_updated":"2021-01-12T08:19:41Z","oa_version":"None","article_processing_charge":"No","abstract":[{"lang":"eng","text":"In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$ be a 2-dimensional torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ > 0. Our main result says that for a 'generic' time-periodic perturbation of an integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad \\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a 'connected' net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7]."}],"keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"year":"2015","doi":"10.1088/0951-7715/28/8/2699","_id":"8498","type":"journal_article","date_created":"2020-09-18T10:46:43Z","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Kaloshin, V., & Zhang, K. (2015). Arnold diffusion for smooth convex systems of two and a half degrees of freedom. *Nonlinearity*. IOP Publishing. https://doi.org/10.1088/0951-7715/28/8/2699","chicago":"Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” *Nonlinearity*. IOP Publishing, 2015. https://doi.org/10.1088/0951-7715/28/8/2699.","short":"V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720.","ieee":"V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two and a half degrees of freedom,” *Nonlinearity*, vol. 28, no. 8. IOP Publishing, pp. 2699–2720, 2015.","mla":"Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” *Nonlinearity*, vol. 28, no. 8, IOP Publishing, 2015, pp. 2699–720, doi:10.1088/0951-7715/28/8/2699.","ama":"Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. *Nonlinearity*. 2015;28(8):2699-2720. doi:10.1088/0951-7715/28/8/2699","ista":"Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720."},"title":"Arnold diffusion for smooth convex systems of two and a half degrees of freedom","volume":28,"page":"2699-2720","publication_identifier":{"issn":["0951-7715","1361-6544"]},"month":"06","date_published":"2015-06-30T00:00:00Z","article_type":"original","publication_status":"published","intvolume":" 28","publisher":"IOP Publishing","author":[{"first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","orcid":"0000-0002-6051-2628"},{"last_name":"Zhang","full_name":"Zhang, K","first_name":"K"}],"extern":"1","status":"public"},{"publisher":"Springer Nature","intvolume":" 315","publication_status":"published","status":"public","extern":"1","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"},{"last_name":"Saprykina","first_name":"Maria","full_name":"Saprykina, Maria"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"643-697","citation":{"short":"V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697.","ieee":"V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension,” *Communications in Mathematical Physics*, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012.","mla":"Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” *Communications in Mathematical Physics*, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97, doi:10.1007/s00220-012-1532-x.","ista":"Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 315(3), 643–697.","ama":"Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. *Communications in Mathematical Physics*. 2012;315(3):643-697. doi:10.1007/s00220-012-1532-x","apa":"Kaloshin, V., & Saprykina, M. (2012). An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s00220-012-1532-x","chicago":"Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” *Communications in Mathematical Physics*. Springer Nature, 2012. https://doi.org/10.1007/s00220-012-1532-x."},"title":"An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension","volume":315,"publication_identifier":{"issn":["0010-3616","1432-0916"]},"month":"11","article_type":"original","date_published":"2012-11-01T00:00:00Z","publication":"Communications in Mathematical Physics","date_updated":"2021-01-12T08:19:44Z","oa_version":"None","article_processing_charge":"No","_id":"8502","doi":"10.1007/s00220-012-1532-x","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"abstract":[{"lang":"eng","text":"The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface."}],"year":"2012","date_created":"2020-09-18T10:47:16Z","quality_controlled":"1","type":"journal_article","day":"01","language":[{"iso":"eng"}],"issue":"3"},{"quality_controlled":"1","date_created":"2020-09-18T10:50:20Z","type":"journal_article","_id":"8525","doi":"10.1007/s002200050811","abstract":[{"lang":"eng","text":"Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented."}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"year":"2000","oa_version":"None","article_processing_charge":"No","publication":"Communications in Mathematical Physics","date_updated":"2021-01-12T08:19:52Z","day":"01","language":[{"iso":"eng"}],"status":"public","extern":"1","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628"}],"publisher":"Springer Nature","intvolume":" 211","publication_status":"published","date_published":"2000-04-01T00:00:00Z","month":"04","article_type":"original","publication_identifier":{"issn":["0010-3616","1432-0916"]},"page":"253-271","volume":211,"citation":{"chicago":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” *Communications in Mathematical Physics*. Springer Nature, 2000. https://doi.org/10.1007/s002200050811.","apa":"Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s002200050811","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","ama":"Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. *Communications in Mathematical Physics*. 2000;211:253-271. doi:10.1007/s002200050811","mla":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” *Communications in Mathematical Physics*, vol. 211, Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.","ieee":"V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” *Communications in Mathematical Physics*, vol. 211. Springer Nature, pp. 253–271, 2000.","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271."},"title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"publication":"Nonlinearity","date_updated":"2021-01-12T08:19:53Z","article_processing_charge":"No","oa_version":"None","_id":"8527","doi":"10.1088/0951-7715/10/5/002","year":"1997","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"abstract":[{"text":"We introduce a new potential-theoretic definition of the dimension spectrum of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if and is a Borel probability measure with compact support in , then under almost every linear transformation from to , the q-dimension of the image of is ; in particular, the q-dimension of is preserved provided . We also present results on the preservation of information dimension and pointwise dimension. Finally, for and q > 2 we give examples for which is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions.","lang":"eng"}],"date_created":"2020-09-18T10:50:41Z","quality_controlled":"1","type":"journal_article","day":"19","language":[{"iso":"eng"}],"issue":"5","publisher":"IOP Publishing","intvolume":" 10","publication_status":"published","status":"public","extern":"1","author":[{"last_name":"Hunt","first_name":"Brian R","full_name":"Hunt, Brian R"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1031-1046","citation":{"ieee":"B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” *Nonlinearity*, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997.","short":"B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.","ama":"Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. *Nonlinearity*. 1997;10(5):1031-1046. doi:10.1088/0951-7715/10/5/002","ista":"Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046.","mla":"Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” *Nonlinearity*, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:10.1088/0951-7715/10/5/002.","chicago":"Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” *Nonlinearity*. IOP Publishing, 1997. https://doi.org/10.1088/0951-7715/10/5/002.","apa":"Hunt, B. R., & Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. *Nonlinearity*. IOP Publishing. https://doi.org/10.1088/0951-7715/10/5/002"},"title":"How projections affect the dimension spectrum of fractal measures","volume":10,"publication_identifier":{"issn":["0951-7715","1361-6544"]},"article_type":"original","date_published":"1997-06-19T00:00:00Z","month":"06"}]