[{"day":"01","type":"journal_article","intvolume":"        62","status":"public","issue":"10","publication":"Journal of Mathematical Physics","month":"10","date_published":"2021-10-01T00:00:00Z","article_type":"original","publisher":"AIP Publishing","scopus_import":"1","language":[{"iso":"eng"}],"department":[{"_id":"MiLe"}],"date_created":"2021-10-24T22:01:32Z","publication_status":"published","citation":{"mla":"Runkel, Ingo, and Lorant Szegedy. “Topological Field Theory on R-Spin Surfaces and the Arf-Invariant.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 10, 102302, AIP Publishing, 2021, doi:<a href=\"https://doi.org/10.1063/5.0037826\">10.1063/5.0037826</a>.","ama":"Runkel I, Szegedy L. Topological field theory on r-spin surfaces and the Arf-invariant. <i>Journal of Mathematical Physics</i>. 2021;62(10). doi:<a href=\"https://doi.org/10.1063/5.0037826\">10.1063/5.0037826</a>","ista":"Runkel I, Szegedy L. 2021. Topological field theory on r-spin surfaces and the Arf-invariant. Journal of Mathematical Physics. 62(10), 102302.","short":"I. Runkel, L. Szegedy, Journal of Mathematical Physics 62 (2021).","apa":"Runkel, I., &#38; Szegedy, L. (2021). Topological field theory on r-spin surfaces and the Arf-invariant. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0037826\">https://doi.org/10.1063/5.0037826</a>","ieee":"I. Runkel and L. Szegedy, “Topological field theory on r-spin surfaces and the Arf-invariant,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 10. AIP Publishing, 2021.","chicago":"Runkel, Ingo, and Lorant Szegedy. “Topological Field Theory on R-Spin Surfaces and the Arf-Invariant.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2021. <a href=\"https://doi.org/10.1063/5.0037826\">https://doi.org/10.1063/5.0037826</a>."},"abstract":[{"lang":"eng","text":"We give a combinatorial model for r-spin surfaces with parameterized boundary based on Novak (“Lattice topological field theories in two dimensions,” Ph.D. thesis, Universität Hamburg, 2015). The r-spin structure is encoded in terms of ℤ𝑟-valued indices assigned to the edges of a polygonal decomposition. This combinatorial model is designed for our state-sum construction of two-dimensional topological field theories on r-spin surfaces. We show that an example of such a topological field theory computes the Arf-invariant of an r-spin surface as introduced by Randal-Williams [J. Topol. 7, 155 (2014)] and Geiges et al. [Osaka J. Math. 49, 449 (2012)]. This implies, in particular, that the r-spin Arf-invariant is constant on orbits of the mapping class group, providing an alternative proof of that fact."}],"author":[{"first_name":"Ingo","last_name":"Runkel","full_name":"Runkel, Ingo"},{"first_name":"Lorant","orcid":"0000-0003-2834-5054","last_name":"Szegedy","full_name":"Szegedy, Lorant","id":"7943226E-220E-11EA-94C7-D59F3DDC885E"}],"arxiv":1,"volume":62,"oa":1,"date_updated":"2023-08-14T08:04:12Z","article_processing_charge":"No","_id":"10176","publication_identifier":{"issn":["00222488"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We would like to thank Nils Carqueville, Tobias Dyckerhoff, Jan Hesse, Ehud Meir, Sebastian Novak, Louis-Hadrien Robert, Nick Salter, Walker Stern, and Lukas Woike for helpful discussions and comments. L.S. was supported by the DFG Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory.”","quality_controlled":"1","oa_version":"Preprint","year":"2021","doi":"10.1063/5.0037826","title":"Topological field theory on r-spin surfaces and the Arf-invariant","external_id":{"isi":["000755638500010"],"arxiv":["1802.09978"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.09978"}],"isi":1,"article_number":"102302"},{"citation":{"short":"S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).","ista":"Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901.","mla":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6, 061901, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>.","ama":"Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. 2020;61(6). doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>","chicago":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>.","apa":"Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>","ieee":"S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. II. Upper bound,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6. AIP Publishing, 2020."},"publication_status":"published","author":[{"first_name":"Simon","last_name":"Mayer","full_name":"Mayer, Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"abstract":[{"lang":"eng","text":"We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality in the asymptotic expansion."}],"article_processing_charge":"No","date_updated":"2023-08-22T08:12:40Z","oa":1,"volume":61,"arxiv":1,"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"oa_version":"Preprint","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["00222488"]},"_id":"8134","ec_funded":1,"year":"2020","doi":"10.1063/5.0005950","title":"The free energy of the two-dimensional dilute Bose gas. II. Upper bound","external_id":{"arxiv":["2002.08281"],"isi":["000544595100001"]},"article_number":"061901","isi":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.08281"}],"type":"journal_article","day":"22","status":"public","intvolume":"        61","publication":"Journal of Mathematical Physics","issue":"6","date_published":"2020-06-22T00:00:00Z","article_type":"original","month":"06","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"AIP Publishing","department":[{"_id":"RoSe"}],"date_created":"2020-07-19T22:00:59Z"},{"scopus_import":"1","publisher":"AIP Publishing","language":[{"iso":"eng"}],"month":"10","article_type":"original","date_published":"2020-10-01T00:00:00Z","date_created":"2020-10-18T22:01:36Z","department":[{"_id":"JaMa"}],"intvolume":"        61","status":"public","day":"01","type":"journal_article","publication":"Journal of Mathematical Physics","issue":"10","title":"Equality conditions of data processing inequality for α-z Rényi relative entropies","external_id":{"arxiv":["2007.06644"],"isi":["000578529200001"]},"doi":"10.1063/5.0022787","year":"2020","ec_funded":1,"isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/2007.06644","open_access":"1"}],"article_number":"102201","abstract":[{"text":"The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].","lang":"eng"}],"author":[{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan"}],"citation":{"ista":"Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 61(10), 102201.","short":"H. Zhang, Journal of Mathematical Physics 61 (2020).","ama":"Zhang H. Equality conditions of data processing inequality for α-z Rényi relative entropies. <i>Journal of Mathematical Physics</i>. 2020;61(10). doi:<a href=\"https://doi.org/10.1063/5.0022787\">10.1063/5.0022787</a>","mla":"Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 10, 102201, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/5.0022787\">10.1063/5.0022787</a>.","chicago":"Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/5.0022787\">https://doi.org/10.1063/5.0022787</a>.","apa":"Zhang, H. (2020). Equality conditions of data processing inequality for α-z Rényi relative entropies. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0022787\">https://doi.org/10.1063/5.0022787</a>","ieee":"H. Zhang, “Equality conditions of data processing inequality for α-z Rényi relative entropies,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 10. AIP Publishing, 2020."},"publication_status":"published","publication_identifier":{"issn":["00222488"]},"_id":"8670","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","oa_version":"Preprint","acknowledgement":"This research was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411. The author would like to thank Anna Vershynina and Sarah Chehade for their helpful comments.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"article_processing_charge":"No","date_updated":"2023-08-22T10:32:29Z","oa":1,"volume":61},{"author":[{"first_name":"Vojkan","full_name":"Jaksic, Vojkan","last_name":"Jaksic"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"}],"publication_status":"published","citation":{"apa":"Jaksic, V., &#38; Seiringer, R. (2019). Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.5138135\">https://doi.org/10.1063/1.5138135</a>","ieee":"V. Jaksic and R. Seiringer, “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018,” <i>Journal of Mathematical Physics</i>, vol. 60, no. 12. AIP Publishing, 2019.","chicago":"Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2019. <a href=\"https://doi.org/10.1063/1.5138135\">https://doi.org/10.1063/1.5138135</a>.","ama":"Jaksic V, Seiringer R. Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. <i>Journal of Mathematical Physics</i>. 2019;60(12). doi:<a href=\"https://doi.org/10.1063/1.5138135\">10.1063/1.5138135</a>","mla":"Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018.” <i>Journal of Mathematical Physics</i>, vol. 60, no. 12, 123504, AIP Publishing, 2019, doi:<a href=\"https://doi.org/10.1063/1.5138135\">10.1063/1.5138135</a>.","ista":"Jaksic V, Seiringer R. 2019. Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics. 60(12), 123504.","short":"V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"Published Version","_id":"7226","publication_identifier":{"issn":["00222488"]},"date_updated":"2024-02-28T13:01:45Z","volume":60,"oa":1,"article_processing_charge":"No","external_id":{"isi":["000505529800002"]},"title":"Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018","doi":"10.1063/1.5138135","year":"2019","ddc":["500"],"isi":1,"article_number":"123504","status":"public","intvolume":"        60","type":"journal_article","day":"01","file_date_updated":"2020-07-14T12:47:54Z","issue":"12","publication":"Journal of Mathematical Physics","language":[{"iso":"eng"}],"publisher":"AIP Publishing","scopus_import":"1","date_published":"2019-12-01T00:00:00Z","article_type":"letter_note","month":"12","date_created":"2020-01-05T23:00:46Z","file":[{"access_level":"open_access","date_updated":"2020-07-14T12:47:54Z","file_size":1025015,"file_name":"2019_JournalMathPhysics_Jaksic.pdf","checksum":"bbd12ad1999a9ad7ba4d3c6f2e579c22","date_created":"2020-01-07T14:59:13Z","relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"7244"}],"department":[{"_id":"RoSe"}],"has_accepted_license":"1"},{"issue":"8","publication":" Journal of Mathematical Physics","day":"01","type":"journal_article","intvolume":"        58","status":"public","department":[{"_id":"RoSe"}],"date_created":"2018-12-11T11:49:10Z","month":"08","date_published":"2017-08-01T00:00:00Z","publisher":"AIP Publishing","scopus_import":"1","language":[{"iso":"eng"}],"publist_id":"6531","volume":58,"date_updated":"2024-02-28T13:07:56Z","oa":1,"article_processing_charge":"No","_id":"912","publication_identifier":{"issn":["00222488"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"}],"quality_controlled":"1","publication_status":"published","citation":{"chicago":"Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions at Infinity.” <i> Journal of Mathematical Physics</i>. AIP Publishing, 2017. <a href=\"https://doi.org/10.1063/1.4996580\">https://doi.org/10.1063/1.4996580</a>.","apa":"Deuchert, A. (2017). A lower bound for the BCS functional with boundary conditions at infinity. <i> Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.4996580\">https://doi.org/10.1063/1.4996580</a>","ieee":"A. Deuchert, “A lower bound for the BCS functional with boundary conditions at infinity,” <i> Journal of Mathematical Physics</i>, vol. 58, no. 8. AIP Publishing, 2017.","short":"A. Deuchert,  Journal of Mathematical Physics 58 (2017).","ista":"Deuchert A. 2017. A lower bound for the BCS functional with boundary conditions at infinity.  Journal of Mathematical Physics. 58(8), 081901.","ama":"Deuchert A. A lower bound for the BCS functional with boundary conditions at infinity. <i> Journal of Mathematical Physics</i>. 2017;58(8). doi:<a href=\"https://doi.org/10.1063/1.4996580\">10.1063/1.4996580</a>","mla":"Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions at Infinity.” <i> Journal of Mathematical Physics</i>, vol. 58, no. 8, 081901, AIP Publishing, 2017, doi:<a href=\"https://doi.org/10.1063/1.4996580\">10.1063/1.4996580</a>."},"abstract":[{"text":"We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer (BCS) theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals.\r\n","lang":"eng"}],"author":[{"id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","first_name":"Andreas","full_name":"Deuchert, Andreas","last_name":"Deuchert","orcid":"0000-0003-3146-6746"}],"isi":1,"article_number":"081901","main_file_link":[{"url":"https://arxiv.org/abs/1703.04616","open_access":"1"}],"year":"2017","doi":"10.1063/1.4996580","ec_funded":1,"title":"A lower bound for the BCS functional with boundary conditions at infinity","external_id":{"isi":["000409197200015"]}}]