[{"abstract":[{"lang":"eng","text":"We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Bose–Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution."}],"oa_version":"Published Version","scopus_import":"1","month":"03","intvolume":" 236","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"publication_status":"published","file":[{"date_created":"2020-11-20T13:17:42Z","file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","date_updated":"2020-11-20T13:17:42Z","file_size":704633,"creator":"dernst","file_id":"8785","checksum":"b645fb64bfe95bbc05b3eea374109a9c","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"issue":"6","volume":236,"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","_id":"7650","article_type":"original","type":"journal_article","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)"},"status":"public","date_updated":"2023-09-05T14:18:49Z","ddc":["510"],"file_date_updated":"2020-11-20T13:17:42Z","department":[{"_id":"RoSe"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions. Financial support by the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (Grant Agreement No. 694227) is gratefully acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 836146.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2020","day":"09","publication":"Archive for Rational Mechanics and Analysis","page":"1217-1271","doi":"10.1007/s00205-020-01489-4","date_published":"2020-03-09T00:00:00Z","date_created":"2020-04-08T15:18:03Z","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"citation":{"ista":"Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6), 1217–1271.","chicago":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01489-4.","apa":"Deuchert, A., & Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-020-01489-4","ama":"Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. 2020;236(6):1217-1271. doi:10.1007/s00205-020-01489-4","short":"A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236 (2020) 1217–1271.","ieee":"A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature,” Archive for Rational Mechanics and Analysis, vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.","mla":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis, vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:10.1007/s00205-020-01489-4."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas","last_name":"Deuchert"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000519415000001"],"arxiv":["1901.11363"]},"article_processing_charge":"Yes (via OA deal)","title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606.","chicago":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” Archive for Rational Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01548-w.","ama":"Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. 2020;238(11):541-606. doi:10.1007/s00205-020-01548-w","apa":"Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-020-01548-w","ieee":"L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons,” Archive for Rational Mechanics and Analysis, vol. 238, no. 11. Springer Nature, pp. 541–606, 2020.","short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.","mla":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” Archive for Rational Mechanics and Analysis, vol. 238, no. 11, Springer Nature, 2020, pp. 541–606, doi:10.1007/s00205-020-01548-w."},"title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","author":[{"last_name":"Bossmann","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"}],"external_id":{"arxiv":["1907.04547"],"isi":["000550164400001"]},"article_processing_charge":"Yes (via OA deal)","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"day":"01","publication":"Archive for Rational Mechanics and Analysis","isi":1,"has_accepted_license":"1","year":"2020","date_published":"2020-11-01T00:00:00Z","doi":"10.1007/s00205-020-01548-w","date_created":"2020-07-18T15:06:35Z","page":"541-606","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo and Nikolai Leopold are gratefully acknowledged. This work was supported by the German Research Foundation within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems” and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"ddc":["510"],"date_updated":"2023-09-05T14:19:06Z","department":[{"_id":"RoSe"}],"file_date_updated":"2020-12-02T08:50:38Z","_id":"8130","status":"public","article_type":"original","type":"journal_article","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)"},"file":[{"date_created":"2020-12-02T08:50:38Z","file_name":"2020_ArchiveRatMech_Bossmann.pdf","creator":"dernst","date_updated":"2020-12-02T08:50:38Z","file_size":942343,"file_id":"8826","checksum":"cc67a79a67bef441625fcb1cd031db3d","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"publication_status":"published","volume":238,"issue":"11","ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"We study the dynamics of a system of N interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to an interval of length of order ε. The interaction is non-negative and scaled in such a way that its scattering length is of order ε/N, while its range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein condensation. We prove that condensation is preserved by the N-body dynamics, where the time-evolved condensate wave function is the solution of a two-dimensional non-linear equation. The strength of the non-linearity depends on the scaling parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the scattering length of the interaction. In both cases, the coupling parameter depends on the confining potential.","lang":"eng"}],"month":"11","intvolume":" 238","scopus_import":"1"},{"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227; R.S.) is gratefully acknowledged.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2020","day":"01","publication":"Journal of Statistical Physics","page":"23-33","date_published":"2020-09-01T00:00:00Z","doi":"10.1007/s10955-019-02322-3","date_created":"2020-01-07T09:42:03Z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"ista":"Lieb EH, Seiringer R. 2020. Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. 180, 23–33.","chicago":"Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02322-3.","short":"E.H. Lieb, R. Seiringer, Journal of Statistical Physics 180 (2020) 23–33.","ieee":"E. H. Lieb and R. Seiringer, “Divergence of the effective mass of a polaron in the strong coupling limit,” Journal of Statistical Physics, vol. 180. Springer Nature, pp. 23–33, 2020.","apa":"Lieb, E. H., & Seiringer, R. (2020). Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02322-3","ama":"Lieb EH, Seiringer R. Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. 2020;180:23-33. doi:10.1007/s10955-019-02322-3","mla":"Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” Journal of Statistical Physics, vol. 180, Springer Nature, 2020, pp. 23–33, doi:10.1007/s10955-019-02322-3."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"first_name":"Elliott H.","full_name":"Lieb, Elliott H.","last_name":"Lieb"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000556199700003"]},"title":"Divergence of the effective mass of a polaron in the strong coupling limit","abstract":[{"text":"We consider the Fröhlich model of a polaron, and show that its effective mass diverges in thestrong coupling limit.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"09","intvolume":" 180","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"publication_status":"published","file":[{"file_name":"2020_JourStatPhysics_Lieb.pdf","date_created":"2020-11-19T11:13:55Z","creator":"dernst","file_size":279749,"date_updated":"2020-11-19T11:13:55Z","success":1,"checksum":"1e67bee6728592f7bdcea2ad2d9366dc","file_id":"8774","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"volume":180,"ec_funded":1,"_id":"7235","type":"journal_article","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)"},"status":"public","date_updated":"2023-09-05T14:57:29Z","ddc":["510","530"],"department":[{"_id":"RoSe"}],"file_date_updated":"2020-11-19T11:13:55Z"},{"department":[{"_id":"KrPi"}],"date_updated":"2023-09-05T15:06:40Z","conference":{"start_date":"2020-05-11","end_date":"2020-05-15","name":"EUROCRYPT: Theory and Applications of Cryptographic Techniques"},"type":"conference","status":"public","_id":"7966","ec_funded":1,"volume":12107,"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"isbn":["9783030457266","9783030457273"],"eissn":["1611-3349"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2019/364"}],"alternative_title":["LNCS"],"intvolume":" 12107","month":"05","abstract":[{"text":"For 1≤m≤n, we consider a natural m-out-of-n multi-instance scenario for a public-key encryption (PKE) scheme. An adversary, given n independent instances of PKE, wins if he breaks at least m out of the n instances. In this work, we are interested in the scaling factor of PKE schemes, SF, which measures how well the difficulty of breaking m out of the n instances scales in m. That is, a scaling factor SF=ℓ indicates that breaking m out of n instances is at least ℓ times more difficult than breaking one single instance. A PKE scheme with small scaling factor hence provides an ideal target for mass surveillance. In fact, the Logjam attack (CCS 2015) implicitly exploited, among other things, an almost constant scaling factor of ElGamal over finite fields (with shared group parameters).\r\n\r\nFor Hashed ElGamal over elliptic curves, we use the generic group model to argue that the scaling factor depends on the scheme's granularity. In low granularity, meaning each public key contains its independent group parameter, the scheme has optimal scaling factor SF=m; In medium and high granularity, meaning all public keys share the same group parameter, the scheme still has a reasonable scaling factor SF=√m. Our findings underline that instantiating ElGamal over elliptic curves should be preferred to finite fields in a multi-instance scenario.\r\n\r\nAs our main technical contribution, we derive new generic-group lower bounds of Ω(√(mp)) on the difficulty of solving both the m-out-of-n Gap Discrete Logarithm and the m-out-of-n Gap Computational Diffie-Hellman problem over groups of prime order p, extending a recent result by Yun (EUROCRYPT 2015). We establish the lower bound by studying the hardness of a related computational problem which we call the search-by-hypersurface problem.","lang":"eng"}],"oa_version":"Submitted Version","article_processing_charge":"No","external_id":{"isi":["000828688000016"]},"author":[{"id":"D33D2B18-E445-11E9-ABB7-15F4E5697425","first_name":"Benedikt","last_name":"Auerbach","full_name":"Auerbach, Benedikt","orcid":"0000-0002-7553-6606"},{"full_name":"Giacon, Federico","last_name":"Giacon","first_name":"Federico"},{"full_name":"Kiltz, Eike","last_name":"Kiltz","first_name":"Eike"}],"title":"Everybody’s a target: Scalability in public-key encryption","citation":{"ieee":"B. Auerbach, F. Giacon, and E. Kiltz, “Everybody’s a target: Scalability in public-key encryption,” in Advances in Cryptology – EUROCRYPT 2020, 2020, vol. 12107, pp. 475–506.","short":"B. Auerbach, F. Giacon, E. Kiltz, in:, Advances in Cryptology – EUROCRYPT 2020, Springer Nature, 2020, pp. 475–506.","ama":"Auerbach B, Giacon F, Kiltz E. Everybody’s a target: Scalability in public-key encryption. In: Advances in Cryptology – EUROCRYPT 2020. Vol 12107. Springer Nature; 2020:475-506. doi:10.1007/978-3-030-45727-3_16","apa":"Auerbach, B., Giacon, F., & Kiltz, E. (2020). Everybody’s a target: Scalability in public-key encryption. In Advances in Cryptology – EUROCRYPT 2020 (Vol. 12107, pp. 475–506). Springer Nature. https://doi.org/10.1007/978-3-030-45727-3_16","mla":"Auerbach, Benedikt, et al. “Everybody’s a Target: Scalability in Public-Key Encryption.” Advances in Cryptology – EUROCRYPT 2020, vol. 12107, Springer Nature, 2020, pp. 475–506, doi:10.1007/978-3-030-45727-3_16.","ista":"Auerbach B, Giacon F, Kiltz E. 2020. Everybody’s a target: Scalability in public-key encryption. Advances in Cryptology – EUROCRYPT 2020. EUROCRYPT: Theory and Applications of Cryptographic Techniques, LNCS, vol. 12107, 475–506.","chicago":"Auerbach, Benedikt, Federico Giacon, and Eike Kiltz. “Everybody’s a Target: Scalability in Public-Key Encryption.” In Advances in Cryptology – EUROCRYPT 2020, 12107:475–506. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-45727-3_16."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"682815","name":"Teaching Old Crypto New Tricks","call_identifier":"H2020","_id":"258AA5B2-B435-11E9-9278-68D0E5697425"}],"page":"475-506","date_created":"2020-06-15T07:13:37Z","doi":"10.1007/978-3-030-45727-3_16","date_published":"2020-05-01T00:00:00Z","year":"2020","isi":1,"publication":"Advances in Cryptology – EUROCRYPT 2020","day":"01","oa":1,"quality_controlled":"1","publisher":"Springer Nature"},{"date_updated":"2023-09-05T15:08:26Z","ddc":["000"],"file_date_updated":"2020-10-15T14:28:06Z","department":[{"_id":"ToHe"}],"_id":"8623","conference":{"name":"RV: Runtime Verification","start_date":"2020-10-06","location":"Los Angeles, CA, United States","end_date":"2020-10-09"},"type":"conference","status":"public","publication_status":"published","publication_identifier":{"isbn":["9783030605070","9783030605087"],"eissn":["1611-3349"],"issn":["0302-9743"]},"language":[{"iso":"eng"}],"file":[{"checksum":"00661f9b7034f52e18bf24fa552b8194","file_id":"8665","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2020-10-15T14:28:06Z","file_name":"monitorability.pdf","creator":"esarac","date_updated":"2020-10-15T14:28:06Z","file_size":478148}],"volume":12399,"abstract":[{"text":"We introduce the monitoring of trace properties under assumptions. An assumption limits the space of possible traces that the monitor may encounter. An assumption may result from knowledge about the system that is being monitored, about the environment, or about another, connected monitor. We define monitorability under assumptions and study its theoretical properties. In particular, we show that for every assumption A, the boolean combinations of properties that are safe or co-safe relative to A are monitorable under A. We give several examples and constructions on how an assumption can make a non-monitorable property monitorable, and how an assumption can make a monitorable property monitorable with fewer resources, such as integer registers.","lang":"eng"}],"oa_version":"Submitted Version","alternative_title":["LNCS"],"scopus_import":"1","intvolume":" 12399","month":"10","citation":{"chicago":"Henzinger, Thomas A, and Naci E Sarac. “Monitorability under Assumptions.” In Runtime Verification, 12399:3–18. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-60508-7_1.","ista":"Henzinger TA, Sarac NE. 2020. Monitorability under assumptions. Runtime Verification. RV: Runtime Verification, LNCS, vol. 12399, 3–18.","mla":"Henzinger, Thomas A., and Naci E. Sarac. “Monitorability under Assumptions.” Runtime Verification, vol. 12399, Springer Nature, 2020, pp. 3–18, doi:10.1007/978-3-030-60508-7_1.","ama":"Henzinger TA, Sarac NE. Monitorability under assumptions. In: Runtime Verification. Vol 12399. Springer Nature; 2020:3-18. doi:10.1007/978-3-030-60508-7_1","apa":"Henzinger, T. A., & Sarac, N. E. (2020). Monitorability under assumptions. In Runtime Verification (Vol. 12399, pp. 3–18). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-030-60508-7_1","short":"T.A. Henzinger, N.E. Sarac, in:, Runtime Verification, Springer Nature, 2020, pp. 3–18.","ieee":"T. A. Henzinger and N. E. Sarac, “Monitorability under assumptions,” in Runtime Verification, Los Angeles, CA, United States, 2020, vol. 12399, pp. 3–18."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000728160600001"]},"author":[{"orcid":"0000-0002-2985-7724","full_name":"Henzinger, Thomas A","last_name":"Henzinger","first_name":"Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sarac, Naci E","last_name":"Sarac","id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","first_name":"Naci E"}],"title":"Monitorability under assumptions","project":[{"grant_number":"Z211","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"25F42A32-B435-11E9-9278-68D0E5697425"}],"year":"2020","has_accepted_license":"1","isi":1,"publication":"Runtime Verification","day":"02","page":"3-18","date_created":"2020-10-07T15:05:37Z","date_published":"2020-10-02T00:00:00Z","doi":"10.1007/978-3-030-60508-7_1","acknowledgement":"This research was supported in part by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award).","oa":1,"quality_controlled":"1","publisher":"Springer Nature"}]