[{"oa_version":"Published Version","type":"journal_article","month":"01","abstract":[{"text":"We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15].","lang":"eng"}],"date_updated":"2024-02-05T12:53:21Z","volume":286,"date_created":"2024-02-04T23:00:53Z","acknowledgement":"A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged.","year":"2024","_id":"14931","publication_status":"epub_ahead","oa":1,"date_published":"2024-01-24T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.1016/j.jfa.2024.110320","open_access":"1"}],"status":"public","external_id":{"arxiv":["2301.04894"]},"intvolume":"       286","citation":{"chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>.","ieee":"A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” <i>Journal of Functional Analysis</i>, vol. 286, no. 7. Elsevier, 2024.","short":"A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024).","ama":"Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. 2024;286(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>, vol. 286, no. 7, 110320, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>.","ista":"Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320."},"author":[{"last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer"}],"day":"24","article_number":"110320","arxiv":1,"title":"Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"publication":"Journal of Functional Analysis","article_type":"original","ec_funded":1,"scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","publication_identifier":{"issn":["0022-1236"],"eissn":["1096--0783"]},"doi":"10.1016/j.jfa.2024.110320","quality_controlled":"1","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"issue":"7","language":[{"iso":"eng"}]},{"tmp":{"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)","short":"CC BY (4.0)"},"article_type":"original","article_processing_charge":"Yes (in subscription journal)","ec_funded":1,"scopus_import":"1","publication":"Reviews in Mathematical Physics","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"publisher":"World Scientific Publishing","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"2360005 ","title":"Universality in low-dimensional BCS theory","arxiv":1,"day":"31","author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","last_name":"Henheik"},{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen"},{"last_name":"Roos","first_name":"Barbara","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara"}],"language":[{"iso":"eng"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"quality_controlled":"1","doi":"10.1142/s0129055x2360005x","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"_id":"14542","year":"2023","acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","date_created":"2023-11-15T23:48:14Z","month":"10","oa_version":"Published Version","type":"journal_article","date_updated":"2023-11-20T10:04:38Z","abstract":[{"text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit.","lang":"eng"}],"citation":{"short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023.","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>.","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, 2360005, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>.","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2023). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2023. doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>"},"external_id":{"arxiv":["2301.05621"]},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1142/S0129055X2360005X"}],"date_published":"2023-10-31T00:00:00Z","has_accepted_license":"1","oa":1,"publication_status":"epub_ahead"},{"oa":1,"has_accepted_license":"1","ddc":["000"],"doi":"10.15479/AT:ISTA:12869","date_published":"2023-04-26T00:00:00Z","status":"public","related_material":{"record":[{"relation":"used_in_publication","id":"14505","status":"for_moderation"},{"relation":"used_in_publication","id":"12890","status":"public"}]},"citation":{"apa":"Klausen, F. R., &#38; Lauritsen, A. B. (2023). Research data for: A stochastic cellular automaton model of culture formation. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:12869\">https://doi.org/10.15479/AT:ISTA:12869</a>","mla":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. <i>Research Data for: A Stochastic Cellular Automaton Model of Culture Formation</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:12869\">10.15479/AT:ISTA:12869</a>.","ista":"Klausen FR, Lauritsen AB. 2023. Research data for: A stochastic cellular automaton model of culture formation, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:12869\">10.15479/AT:ISTA:12869</a>.","ama":"Klausen FR, Lauritsen AB. Research data for: A stochastic cellular automaton model of culture formation. 2023. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:12869\">10.15479/AT:ISTA:12869</a>","short":"F.R. Klausen, A.B. Lauritsen, (2023).","chicago":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Research Data for: A Stochastic Cellular Automaton Model of Culture Formation.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/AT:ISTA:12869\">https://doi.org/10.15479/AT:ISTA:12869</a>.","ieee":"F. R. Klausen and A. B. Lauritsen, “Research data for: A stochastic cellular automaton model of culture formation.” Institute of Science and Technology Austria, 2023."},"author":[{"first_name":"Frederik Ravn","last_name":"Klausen","full_name":"Klausen, Frederik Ravn"},{"first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"}],"license":"https://creativecommons.org/publicdomain/zero/1.0/","day":"26","date_updated":"2023-11-13T07:47:29Z","file":[{"date_created":"2023-04-26T12:30:06Z","access_level":"open_access","date_updated":"2023-04-26T12:30:06Z","file_id":"12870","checksum":"85ede12d38bb8d944022a8cba4d719f5","content_type":"application/octet-stream","relation":"main_file","file_size":4567,"creator":"alaurits","success":1,"file_name":"README.md"},{"file_size":732586731,"content_type":"application/x-zip-compressed","relation":"main_file","creator":"alaurits","file_name":"simulations_era=10_flux_varied_europe.zip","success":1,"date_created":"2023-04-26T12:27:34Z","access_level":"open_access","file_id":"12871","date_updated":"2023-04-26T12:27:34Z","checksum":"25bf79452ae895f9c8a20571a096b4c3"},{"file_size":1743893150,"relation":"main_file","content_type":"application/x-zip-compressed","creator":"alaurits","file_name":"simulations_era=10_flux_varied_torus.zip","success":1,"date_created":"2023-04-26T12:29:53Z","access_level":"open_access","file_id":"12872","date_updated":"2023-04-26T12:29:53Z","checksum":"bca48d80ece73eb169aee7211a4a751a"},{"date_created":"2023-04-26T12:29:19Z","access_level":"open_access","file_id":"12873","date_updated":"2023-04-26T12:29:19Z","checksum":"e77a655db15486a387a36362fbf0b665","file_size":878391851,"relation":"main_file","content_type":"application/x-zip-compressed","creator":"alaurits","file_name":"simulations_era=10_R_varied_torus.zip","success":1},{"date_created":"2023-04-26T12:30:05Z","access_level":"open_access","file_id":"12874","date_updated":"2023-04-26T12:30:05Z","checksum":"8556406513adc4aa2e0417f46680f627","file_size":201652478,"relation":"main_file","content_type":"application/x-zip-compressed","creator":"alaurits","file_name":"simulations_era=100.zip","success":1}],"abstract":[{"text":"We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately round cultures get a competitive advantage.  We first analyse the model  with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e. freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity and the central European plain has less clear cultural borders. ","lang":"eng"}],"month":"04","oa_version":"Published Version","type":"research_data","title":"Research data for: A stochastic cellular automaton model of culture formation","file_date_updated":"2023-04-26T12:30:06Z","date_created":"2023-04-26T12:34:49Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Science and Technology Austria","acknowledgement":"FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs. ","year":"2023","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"_id":"12869","article_processing_charge":"No","tmp":{"name":"Creative Commons Public Domain Dedication (CC0 1.0)","short":"CC0 (1.0)","image":"/images/cc_0.png","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode"}},{"arxiv":1,"title":"Stochastic cellular automaton model of culture formation","article_number":"054307","day":"08","author":[{"full_name":"Klausen, Frederik Ravn","last_name":"Klausen","first_name":"Frederik Ravn"},{"first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"Physical Review E","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","doi":"10.1103/PhysRevE.108.054307","publication_identifier":{"eissn":["2470-0053"],"issn":["2470-0045"]},"language":[{"iso":"eng"}],"issue":"5","date_created":"2023-05-04T08:35:01Z","volume":108,"abstract":[{"lang":"eng","text":"We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately geometrically round cultures get a competitive advantage. We first analyze the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e., freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely, that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity, and the central European plain has less clear cultural borders."}],"date_updated":"2023-11-13T07:47:30Z","type":"journal_article","month":"11","oa_version":"Preprint","_id":"12890","year":"2023","acknowledgement":"Thanks to Kim Sneppen, Svend Krøjer, Peter Wildemann, Peter Rasmussen and Kent Bækgaard Lauritsen for discussions and suggestions. FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.02153"}],"date_published":"2023-11-08T00:00:00Z","publication_status":"published","oa":1,"citation":{"chicago":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” <i>Physical Review E</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">https://doi.org/10.1103/PhysRevE.108.054307</a>.","ieee":"F. R. Klausen and A. B. Lauritsen, “Stochastic cellular automaton model of culture formation,” <i>Physical Review E</i>, vol. 108, no. 5. American Physical Society, 2023.","short":"F.R. Klausen, A.B. Lauritsen, Physical Review E 108 (2023).","ama":"Klausen FR, Lauritsen AB. Stochastic cellular automaton model of culture formation. <i>Physical Review E</i>. 2023;108(5). doi:<a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">10.1103/PhysRevE.108.054307</a>","apa":"Klausen, F. R., &#38; Lauritsen, A. B. (2023). Stochastic cellular automaton model of culture formation. <i>Physical Review E</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">https://doi.org/10.1103/PhysRevE.108.054307</a>","ista":"Klausen FR, Lauritsen AB. 2023. Stochastic cellular automaton model of culture formation. Physical Review E. 108(5), 054307.","mla":"Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” <i>Physical Review E</i>, vol. 108, no. 5, 054307, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/PhysRevE.108.054307\">10.1103/PhysRevE.108.054307</a>."},"intvolume":"       108","related_material":{"link":[{"url":"https://github.com/FrederikRavnKlausen/model-for-culture-formation","relation":"software"}],"record":[{"relation":"research_data","status":"public","id":"12869"}]},"external_id":{"arxiv":["2305.02153"]},"status":"public"},{"file_date_updated":"2022-08-08T07:36:34Z","date_created":"2022-08-05T11:36:56Z","volume":189,"date_updated":"2023-09-05T14:57:49Z","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."}],"month":"07","type":"journal_article","oa_version":"Published Version","_id":"11732","year":"2022","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)","ddc":["530"],"date_published":"2022-07-29T00:00:00Z","has_accepted_license":"1","publication_status":"published","oa":1,"citation":{"ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. 2022;189. doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>","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.” <i>Journal of Statistical Physics</i>, vol. 189, 5, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>.","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2022). The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” <i>Journal of Statistical Physics</i>, vol. 189. Springer Nature, 2022.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022)."},"intvolume":"       189","external_id":{"isi":["000833007200002"]},"status":"public","title":"The BCS energy gap at high density","article_number":"5","day":"29","file":[{"access_level":"open_access","date_created":"2022-08-08T07:36:34Z","checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746","date_updated":"2022-08-08T07:36:34Z","creator":"dernst","file_size":419563,"relation":"main_file","content_type":"application/pdf","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","success":1}],"author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha"},{"first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard"}],"scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","article_type":"original","tmp":{"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)","short":"CC BY (4.0)"},"publication":"Journal of Statistical Physics","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"publisher":"Springer Nature","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","doi":"10.1007/s10955-022-02965-9","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"language":[{"iso":"eng"}],"isi":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}]},{"ddc":["510"],"date_published":"2021-02-12T00:00:00Z","oa":1,"publication_status":"published","has_accepted_license":"1","intvolume":"       111","citation":{"ieee":"A. B. Lauritsen, “The BCS energy gap at low density,” <i>Letters in Mathematical Physics</i>, vol. 111. Springer Nature, 2021.","chicago":"Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11005-021-01358-5\">https://doi.org/10.1007/s11005-021-01358-5</a>.","short":"A.B. Lauritsen, Letters in Mathematical Physics 111 (2021).","ama":"Lauritsen AB. The BCS energy gap at low density. <i>Letters in Mathematical Physics</i>. 2021;111. doi:<a href=\"https://doi.org/10.1007/s11005-021-01358-5\">10.1007/s11005-021-01358-5</a>","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.” <i>Letters in Mathematical Physics</i>, vol. 111, 20, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s11005-021-01358-5\">10.1007/s11005-021-01358-5</a>.","apa":"Lauritsen, A. B. (2021). The BCS energy gap at low density. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-021-01358-5\">https://doi.org/10.1007/s11005-021-01358-5</a>"},"status":"public","external_id":{"isi":["000617531900001"]},"volume":111,"date_created":"2021-02-15T09:27:14Z","file_date_updated":"2021-02-15T09:31:07Z","date_updated":"2023-09-05T15:17:16Z","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"}],"month":"02","oa_version":"Published Version","type":"journal_article","_id":"9121","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)","year":"2021","doi":"10.1007/s11005-021-01358-5","quality_controlled":"1","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"isi":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"title":"The BCS energy gap at low density","article_number":"20","author":[{"full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen"}],"day":"12","file":[{"file_name":"2021_LettersMathPhysics_Lauritsen.pdf","success":1,"file_size":329332,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"9122","date_updated":"2021-02-15T09:31:07Z","checksum":"eaf1b3ff5026f120f0929a5c417dc842","date_created":"2021-02-15T09:31:07Z","access_level":"open_access"}],"publication":"Letters in Mathematical Physics","article_processing_charge":"Yes (via OA deal)","article_type":"original","tmp":{"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)","short":"CC BY (4.0)"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Springer Nature","department":[{"_id":"GradSch"}]},{"title":"Floating Wigner crystal and periodic jellium configurations","arxiv":1,"article_number":"083305","day":"01","file":[{"file_name":"2021_JMathPhy_Lauritsen.pdf","success":1,"file_size":4352640,"relation":"main_file","content_type":"application/pdf","creator":"cziletti","file_id":"10188","date_updated":"2021-10-27T12:57:06Z","checksum":"d035be2b894c4d50d90ac5ce252e27cd","date_created":"2021-10-27T12:57:06Z","access_level":"open_access"}],"author":[{"first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard"}],"scopus_import":"1","article_processing_charge":"No","tmp":{"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)","short":"CC BY (4.0)"},"article_type":"original","publication":"Journal of Mathematical Physics","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"publisher":"AIP Publishing","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","doi":"10.1063/5.0053494","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"language":[{"iso":"eng"}],"issue":"8","isi":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"file_date_updated":"2021-10-27T12:57:06Z","date_created":"2021-08-12T07:08:36Z","volume":62,"date_updated":"2023-08-11T10:29:48Z","abstract":[{"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.","lang":"eng"}],"month":"08","oa_version":"Published Version","type":"journal_article","_id":"9891","year":"2021","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.","ddc":["530"],"date_published":"2021-08-01T00:00:00Z","has_accepted_license":"1","publication_status":"published","oa":1,"citation":{"ama":"Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. 2021;62(8). doi:<a href=\"https://doi.org/10.1063/5.0053494\">10.1063/5.0053494</a>","ista":"Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305.","mla":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:<a href=\"https://doi.org/10.1063/5.0053494\">10.1063/5.0053494</a>.","apa":"Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0053494\">https://doi.org/10.1063/5.0053494</a>","ieee":"A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8. AIP Publishing, 2021.","chicago":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2021. <a href=\"https://doi.org/10.1063/5.0053494\">https://doi.org/10.1063/5.0053494</a>.","short":"A.B. Lauritsen, Journal of Mathematical Physics 62 (2021)."},"intvolume":"        62","status":"public","external_id":{"isi":["000683960800003"],"arxiv":["2103.07975"]}}]