[{"oa_version":"Published Version","citation":{"mla":"Mayer, Simon. *The Free Energy of a Dilute Two-Dimensional Bose Gas*. IST Austria, 2020, doi:10.15479/AT:ISTA:7514.","chicago":"Mayer, Simon. *The Free Energy of a Dilute Two-Dimensional Bose Gas*. IST Austria, 2020. https://doi.org/10.15479/AT:ISTA:7514.","ieee":"S. Mayer, *The free energy of a dilute two-dimensional Bose gas*. IST Austria, 2020.","ista":"Mayer S. 2020. The free energy of a dilute two-dimensional Bose gas, IST Austria, 148p.","apa":"Mayer, S. (2020). *The free energy of a dilute two-dimensional Bose gas*. IST Austria. https://doi.org/10.15479/AT:ISTA:7514","ama":"Mayer S. *The Free Energy of a Dilute Two-Dimensional Bose Gas*. IST Austria; 2020. doi:10.15479/AT:ISTA:7514","short":"S. Mayer, The Free Energy of a Dilute Two-Dimensional Bose Gas, IST Austria, 2020."},"publisher":"IST Austria","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"accept":"1","creator":{"id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","login":"dernst"},"page":"148","_version":5,"date_created":"2020-02-24T09:17:27Z","date_published":"2020-02-24T00:00:00Z","file_date_updated":"2020-02-24T09:15:16Z","oa":1,"title":"The free energy of a dilute two-dimensional Bose gas","publication_status":"published","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"RoSe"}],"abstract":[{"lang":"eng","text":"We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case.\r\nWe motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks."}],"author":[{"first_name":"Simon","last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","full_name":"Mayer, Simon"}],"date_updated":"2020-02-26T09:11:39Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7514","year":"2020","doi":"10.15479/AT:ISTA:7514","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"7524"}]},"file":[{"relation":"main_file","date_created":"2020-02-24T09:15:06Z","file_name":"thesis.pdf","date_updated":"2020-02-24T09:15:06Z","content_type":"application/pdf","file_size":1563429,"success":1,"access_level":"open_access","creator":"dernst","open_access":1,"file_id":"7515"},{"file_name":"thesis_source.zip","date_updated":"2020-02-24T09:15:16Z","relation":"source_file","date_created":"2020-02-24T09:15:16Z","request_a_copy":0,"file_size":2028038,"content_type":"application/x-zip-compressed","access_level":"closed","creator":"dernst","open_access":0,"file_id":"7516"}],"language":[{"iso":"eng"}],"supervisor":[{"full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"day":"24","alternative_title":["IST Austria Thesis"],"type":"dissertation","month":"02","article_processing_charge":"No","ddc":["510"],"cc_license":"cc_by","status":"public","publication_identifier":{"issn":["2663-337X"]}},{"oa_version":"Published Version","publisher":"Springer Nature","citation":{"short":"L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics (2020).","ama":"Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the mean-field description of the dynamics of interacting bosons. *Journal of Statistical Physics*. 2020. doi:10.1007/s10955-020-02500-8","apa":"Bossmann, L., Pavlović, N., Pickl, P., & Soffer, A. (2020). Higher order corrections to the mean-field description of the dynamics of interacting bosons. *Journal of Statistical Physics*. https://doi.org/10.1007/s10955-020-02500-8","ista":"Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics.","ieee":"L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections to the mean-field description of the dynamics of interacting bosons,” *Journal of Statistical Physics*, 2020.","chicago":"Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” *Journal of Statistical Physics*, 2020. https://doi.org/10.1007/s10955-020-02500-8.","mla":"Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” *Journal of Statistical Physics*, Springer Nature, 2020, doi:10.1007/s10955-020-02500-8."},"publication":"Journal of Statistical Physics","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"}],"accept":"1","creator":{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","login":"lbossman"},"_version":4,"quality_controlled":"1","date_created":"2020-02-23T09:45:51Z","date_published":"2020-02-21T00:00:00Z","file_date_updated":"2020-02-24T14:17:24Z","oa":1,"title":"Higher order corrections to the mean-field description of the dynamics of interacting bosons","publication_status":"published","department":[{"_id":"RoSe","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"abstract":[{"text":"In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N d-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision in powers of N−1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.","lang":"eng"}],"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","last_name":"Bossmann","first_name":"Lea","orcid":"0000-0002-6854-1343","full_name":"Bossmann, Lea"},{"full_name":"Pavlović, Nataša","first_name":"Nataša","last_name":"Pavlović"},{"full_name":"Pickl, Peter","last_name":"Pickl","first_name":"Peter"},{"last_name":"Soffer","first_name":"Avy","full_name":"Soffer, Avy"}],"date_updated":"2020-02-27T12:38:44Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"7508","external_id":{"arxiv":["1905.06164"]},"doi":"10.1007/s10955-020-02500-8","year":"2020","file":[{"creator":"dernst","file_id":"7518","open_access":1,"success":1,"access_level":"open_access","content_type":"application/pdf","file_size":587276,"relation":"main_file","date_created":"2020-02-24T14:17:24Z","date_updated":"2020-02-24T14:17:24Z","file_name":"2020_JournStatisticPhysics_Bossmann.pdf"}],"language":[{"iso":"eng"}],"day":"21","type":"journal_article","month":"02","article_type":"original","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"cc_license":"cc_by","status":"public","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]}},{"creator":{"login":"srademac","id":"856966FE-A408-11E9-977E-802DE6697425"},"language":[{"iso":"eng"}],"day":"12","oa_version":"Published Version","date_updated":"2020-03-23T14:08:57Z","citation":{"ista":"Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics.","short":"S.A.E. Rademacher, Letters in Mathematical Physics (2020).","ama":"Rademacher SAE. Central limit theorem for Bose gases interacting through singular potentials. *Letters in Mathematical Physics*. 2020. doi:10.1007/s11005-020-01286-w","apa":"Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting through singular potentials. *Letters in Mathematical Physics*. https://doi.org/10.1007/s11005-020-01286-w","mla":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” *Letters in Mathematical Physics*, Springer Nature, 2020, doi:10.1007/s11005-020-01286-w.","ieee":"S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through singular potentials,” *Letters in Mathematical Physics*, 2020.","chicago":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” *Letters in Mathematical Physics*, 2020. https://doi.org/10.1007/s11005-020-01286-w."},"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7611","publication":"Letters in Mathematical Physics","year":"2020","doi":"10.1007/s11005-020-01286-w","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"publication_status":"epub_ahead","article_type":"original","article_processing_charge":"No","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"RoSe"}],"abstract":[{"text":"We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.","lang":"eng"}],"status":"public","publication_identifier":{"issn":["0377-9017","1573-0530"]},"author":[{"full_name":"Rademacher, Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","last_name":"Rademacher"}],"type":"journal_article","quality_controlled":"1","_version":2,"month":"03","date_created":"2020-03-23T11:11:47Z","date_published":"2020-03-12T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.1007/s11005-020-01286-w","open_access":"1"}],"oa":1,"title":"Central limit theorem for Bose gases interacting through singular potentials"},{"language":[{"iso":"eng"}],"issue":"2","day":"01","file":[{"open_access":1,"file_id":"5688","creator":"dernst","access_level":"open_access","success":1,"file_size":893902,"content_type":"application/pdf","date_created":"2018-12-17T10:34:06Z","relation":"main_file","date_updated":"2018-12-17T10:34:06Z","file_name":"2018_CommunMathPhys_Deuchert.pdf"}],"doi":"10.1007/s00220-018-3239-0","year":"2019","_id":"80","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","date_updated":"2020-01-21T13:22:16Z","status":"public","ddc":["530"],"cc_license":"cc_by","article_type":"original","article_processing_charge":"Yes (via OA deal)","volume":368,"month":"06","type":"journal_article","creator":{"id":"2EBD1598-F248-11E8-B48F-1D18A9856A87","login":"patrickd"},"page":"723-776","intvolume":" 368","accept":"1","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27"}],"publication":"Communications in Mathematical Physics","citation":{"apa":"Deuchert, A., Seiringer, R., & Yngvason, J. (2019). Bose–Einstein condensation in a dilute, trapped gas at positive temperature. *Communications in Mathematical Physics*, *368*(2), 723–776. https://doi.org/10.1007/s00220-018-3239-0","ama":"Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. *Communications in Mathematical Physics*. 2019;368(2):723-776. doi:10.1007/s00220-018-3239-0","short":"A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 368 (2019) 723–776.","ista":"Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. 368(2), 723–776.","chicago":"Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” *Communications in Mathematical Physics* 368, no. 2 (2019): 723–76. https://doi.org/10.1007/s00220-018-3239-0.","ieee":"A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in a dilute, trapped gas at positive temperature,” *Communications in Mathematical Physics*, vol. 368, no. 2, pp. 723–776, 2019.","mla":"Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” *Communications in Mathematical Physics*, vol. 368, no. 2, Springer, 2019, pp. 723–76, doi:10.1007/s00220-018-3239-0."},"publisher":"Springer","publist_id":"7974","oa_version":"Published Version","author":[{"full_name":"Deuchert, Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","first_name":"Andreas","last_name":"Deuchert"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer"},{"last_name":"Yngvason","first_name":"Jakob","full_name":"Yngvason, Jakob"}],"abstract":[{"text":"We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.","lang":"eng"}],"department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"RoSe"}],"publication_status":"published","oa":1,"file_date_updated":"2018-12-17T10:34:06Z","title":"Bose–Einstein condensation in a dilute, trapped gas at positive temperature","date_published":"2019-06-01T00:00:00Z","_version":17,"quality_controlled":"1","date_created":"2018-12-11T11:44:31Z"},{"publication":"Journal of Statistical Mechanics: Theory and Experiment","project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"oa_version":"Preprint","publisher":"IOP Publishing","citation":{"ama":"Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. *Journal of Statistical Mechanics: Theory and Experiment*. 2019;2019(6). doi:10.1088/1742-5468/ab190d","apa":"Mysliwy, K., & Napiórkowski, M. (2019). Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. *Journal of Statistical Mechanics: Theory and Experiment*, *2019*(6). https://doi.org/10.1088/1742-5468/ab190d","short":"K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019).","ista":"Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063101.","chicago":"Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” *Journal of Statistical Mechanics: Theory and Experiment* 2019, no. 6 (2019). https://doi.org/10.1088/1742-5468/ab190d.","ieee":"K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps,” *Journal of Statistical Mechanics: Theory and Experiment*, vol. 2019, no. 6, 2019.","mla":"Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” *Journal of Statistical Mechanics: Theory and Experiment*, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:10.1088/1742-5468/ab190d."},"creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"intvolume":" 2019","date_published":"2019-06-13T00:00:00Z","title":"Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1810.02209","open_access":"1"}],"date_created":"2019-09-01T22:00:59Z","quality_controlled":"1","_version":7,"abstract":[{"text":"We discuss thermodynamic properties of harmonically trapped\r\nimperfect quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition of the mean-field interparticle potential energy as compared\r\nto the homogeneous case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments that this model corresponds to the limiting case of\r\na long-ranged interparticle potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation similar to the well-known Kac scaling\r\nprocedure, which is presented here in a form adapted to the case of an isotropic\r\nharmonic trap. We show that within the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein condensation provided d > 1.\r\nThe main result of our analysis is that in d = 1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill\r\nthe relation aB + aF = \u001f. This result supplements similar recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform imperfect\r\nrepulsive Bose and attractive Fermi gases.","lang":"eng"}],"author":[{"id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof","last_name":"Mysliwy","full_name":"Mysliwy, Krzysztof"},{"first_name":"Marek","last_name":"Napiórkowski","full_name":"Napiórkowski, Marek"}],"publication_status":"published","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"RoSe"}],"external_id":{"arxiv":["1810.02209"]},"_id":"6840","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2019","doi":"10.1088/1742-5468/ab190d","date_updated":"2020-01-21T12:04:50Z","day":"13","issue":"6","language":[{"iso":"eng"}],"article_number":"063101","volume":2019,"type":"journal_article","month":"06","status":"public","publication_identifier":{"eissn":["1742-5468"]}}]