[{"publication":"Forum of Mathematics, Sigma","article_processing_charge":"No","ec_funded":1,"scopus_import":"1","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)"},"publisher":"Cambridge University Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"RoSe"}],"arxiv":1,"title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","article_number":"e20","author":[{"last_name":"Deuchert","first_name":"Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","full_name":"Deuchert, Andreas"},{"full_name":"Mayer, Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","last_name":"Mayer","first_name":"Simon"},{"last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"file":[{"file_name":"2020_ForumMath_Deuchert.pdf","creator":"dernst","file_size":692530,"content_type":"application/pdf","relation":"main_file","checksum":"8a64da99d107686997876d7cad8cfe1e","file_id":"7797","date_updated":"2020-07-14T12:48:03Z","access_level":"open_access","date_created":"2020-05-04T12:02:41Z"}],"day":"14","isi":1,"language":[{"iso":"eng"}],"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"doi":"10.1017/fms.2020.17","quality_controlled":"1","publication_identifier":{"eissn":["20505094"]},"_id":"7790","year":"2020","volume":8,"date_created":"2020-05-03T22:00:48Z","file_date_updated":"2020-07-14T12:48:03Z","date_updated":"2023-08-21T06:18:49Z","abstract":[{"text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 .","lang":"eng"}],"month":"03","oa_version":"Published Version","type":"journal_article","related_material":{"record":[{"relation":"earlier_version","id":"7524","status":"public"}]},"intvolume":"         8","citation":{"short":"A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>","ista":"Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>.","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>"},"status":"public","external_id":{"arxiv":["1910.03372"],"isi":["000527342000001"]},"date_published":"2020-03-14T00:00:00Z","ddc":["510"],"oa":1,"publication_status":"published","has_accepted_license":"1"},{"article_processing_charge":"No","ec_funded":1,"article_type":"original","publication":"The Journal of Chemical Physics","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"AIP Publishing","title":"Intermolecular forces and correlations mediated by a phonon bath","arxiv":1,"article_number":"164302","day":"27","author":[{"id":"4B7E523C-F248-11E8-B48F-1D18A9856A87","full_name":"Li, Xiang","first_name":"Xiang","last_name":"Li"},{"full_name":"Yakaboylu, Enderalp","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5973-0874","last_name":"Yakaboylu","first_name":"Enderalp"},{"first_name":"Giacomo","last_name":"Bighin","id":"4CA96FD4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8823-9777","full_name":"Bighin, Giacomo"},{"first_name":"Richard","last_name":"Schmidt","full_name":"Schmidt, Richard"},{"last_name":"Lemeshko","first_name":"Mikhail","orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Lemeshko, Mikhail"},{"first_name":"Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas"}],"language":[{"iso":"eng"}],"issue":"16","isi":1,"keyword":["Physical and Theoretical Chemistry","General Physics and Astronomy"],"project":[{"grant_number":"P29902","name":"Quantum rotations in the presence of a many-body environment","call_identifier":"FWF","_id":"26031614-B435-11E9-9278-68D0E5697425"},{"grant_number":"801770","_id":"2688CF98-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Angulon: physics and applications of a new quasiparticle"},{"grant_number":"M02641","name":"A path-integral approach to composite impurities","_id":"26986C82-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"quality_controlled":"1","doi":"10.1063/1.5144759","publication_identifier":{"eissn":["1089-7690"],"issn":["0021-9606"]},"_id":"8587","year":"2020","acknowledgement":"We are grateful to Areg Ghazaryan for valuable discussions. M.L. acknowledges support from the Austrian Science Fund (FWF) under Project No. P29902-N27 and from the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). G.B. acknowledges support from the Austrian Science Fund (FWF) under Project No. M2461-N27. A.D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the European Research Council (ERC) Grant Agreement No. 694227 and under the Marie Sklodowska-Curie Grant Agreement No. 836146. R.S. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2111 – 390814868.","date_created":"2020-09-30T10:33:17Z","volume":152,"abstract":[{"text":"Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born–Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.","lang":"eng"}],"date_updated":"2024-08-07T07:16:53Z","type":"journal_article","month":"04","oa_version":"Preprint","citation":{"ama":"Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. Intermolecular forces and correlations mediated by a phonon bath. <i>The Journal of Chemical Physics</i>. 2020;152(16). doi:<a href=\"https://doi.org/10.1063/1.5144759\">10.1063/1.5144759</a>","mla":"Li, Xiang, et al. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” <i>The Journal of Chemical Physics</i>, vol. 152, no. 16, 164302, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/1.5144759\">10.1063/1.5144759</a>.","ista":"Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. 2020. Intermolecular forces and correlations mediated by a phonon bath. The Journal of Chemical Physics. 152(16), 164302.","apa":"Li, X., Yakaboylu, E., Bighin, G., Schmidt, R., Lemeshko, M., &#38; Deuchert, A. (2020). Intermolecular forces and correlations mediated by a phonon bath. <i>The Journal of Chemical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.5144759\">https://doi.org/10.1063/1.5144759</a>","ieee":"X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, and A. Deuchert, “Intermolecular forces and correlations mediated by a phonon bath,” <i>The Journal of Chemical Physics</i>, vol. 152, no. 16. AIP Publishing, 2020.","chicago":"Li, Xiang, Enderalp Yakaboylu, Giacomo Bighin, Richard Schmidt, Mikhail Lemeshko, and Andreas Deuchert. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” <i>The Journal of Chemical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/1.5144759\">https://doi.org/10.1063/1.5144759</a>.","short":"X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, A. Deuchert, The Journal of Chemical Physics 152 (2020)."},"intvolume":"       152","related_material":{"record":[{"relation":"dissertation_contains","id":"8958","status":"public"}]},"external_id":{"isi":["000530448300001"],"arxiv":["1912.02658"]},"status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1912.02658"}],"date_published":"2020-04-27T00:00:00Z","publication_status":"published","oa":1},{"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","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":"Archive for Rational Mechanics and Analysis","department":[{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Springer Nature","arxiv":1,"title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","day":"09","file":[{"checksum":"b645fb64bfe95bbc05b3eea374109a9c","date_updated":"2020-11-20T13:17:42Z","file_id":"8785","access_level":"open_access","date_created":"2020-11-20T13:17:42Z","success":1,"file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":704633}],"author":[{"first_name":"Andreas","last_name":"Deuchert","full_name":"Deuchert, Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"}],"language":[{"iso":"eng"}],"issue":"6","isi":1,"project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","doi":"10.1007/s00205-020-01489-4","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"_id":"7650","year":"2020","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.","file_date_updated":"2020-11-20T13:17:42Z","date_created":"2020-04-08T15:18:03Z","volume":236,"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."}],"date_updated":"2023-09-05T14:18:49Z","type":"journal_article","oa_version":"Published Version","month":"03","page":"1217-1271","citation":{"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,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.","chicago":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>.","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.","mla":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>.","apa":"Deuchert, A., &#38; Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>","ama":"Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271. doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>"},"intvolume":"       236","status":"public","external_id":{"arxiv":["1901.11363"],"isi":["000519415000001"]},"date_published":"2020-03-09T00:00:00Z","ddc":["510"],"has_accepted_license":"1","publication_status":"published","oa":1},{"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","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":"Communications in Mathematical Physics","department":[{"_id":"RoSe"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer","publist_id":"7974","title":"Bose–Einstein condensation in a dilute, trapped gas at positive temperature","day":"01","file":[{"date_created":"2018-12-17T10:34:06Z","access_level":"open_access","file_id":"5688","date_updated":"2020-07-14T12:48:07Z","checksum":"c7e9880b43ac726712c1365e9f2f73a6","file_size":893902,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_name":"2018_CommunMathPhys_Deuchert.pdf"}],"author":[{"orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","full_name":"Deuchert, Andreas","first_name":"Andreas","last_name":"Deuchert"},{"first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert"},{"full_name":"Yngvason, Jakob","last_name":"Yngvason","first_name":"Jakob"}],"language":[{"iso":"eng"}],"issue":"2","isi":1,"project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27"}],"quality_controlled":"1","doi":"10.1007/s00220-018-3239-0","_id":"80","year":"2019","file_date_updated":"2020-07-14T12:48:07Z","date_created":"2018-12-11T11:44:31Z","volume":368,"date_updated":"2023-08-24T14:27:51Z","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","type":"journal_article","month":"06","page":"723-776","citation":{"ama":"Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. <i>Communications in Mathematical Physics</i>. 2019;368(2):723-776. doi:<a href=\"https://doi.org/10.1007/s00220-018-3239-0\">10.1007/s00220-018-3239-0</a>","mla":"Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” <i>Communications in Mathematical Physics</i>, vol. 368, no. 2, Springer, 2019, pp. 723–76, doi:<a href=\"https://doi.org/10.1007/s00220-018-3239-0\">10.1007/s00220-018-3239-0</a>.","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.","apa":"Deuchert, A., Seiringer, R., &#38; Yngvason, J. (2019). Bose–Einstein condensation in a dilute, trapped gas at positive temperature. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-018-3239-0\">https://doi.org/10.1007/s00220-018-3239-0</a>","ieee":"A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in a dilute, trapped gas at positive temperature,” <i>Communications in Mathematical Physics</i>, vol. 368, no. 2. Springer, pp. 723–776, 2019.","chicago":"Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” <i>Communications in Mathematical Physics</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00220-018-3239-0\">https://doi.org/10.1007/s00220-018-3239-0</a>.","short":"A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 368 (2019) 723–776."},"intvolume":"       368","external_id":{"isi":["000467796800007"]},"status":"public","date_published":"2019-06-01T00:00:00Z","ddc":["530"],"has_accepted_license":"1","oa":1,"publication_status":"published"},{"main_file_link":[{"url":"https://arxiv.org/abs/1910.03372","open_access":"1"}],"date_published":"2019-10-08T00:00:00Z","publication_status":"draft","oa":1,"citation":{"ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv:191003372</i>.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv:1910.03372</i>. ArXiv.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv:1910.03372</i>, ArXiv.","ista":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, .","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv:1910.03372</i>. ArXiv, n.d.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>arXiv:1910.03372</i>. ArXiv.","short":"A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.)."},"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"7790"},{"status":"public","id":"7514","relation":"dissertation_contains"}]},"status":"public","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"date_created":"2020-02-26T08:46:40Z","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","month":"10","oa_version":"Preprint","type":"preprint","date_updated":"2023-09-07T13:12:41Z","abstract":[{"lang":"eng","text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$ and inverse temperature $\\beta$ differs from the one of the non-interacting system by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ = \\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho \\ll 1$ and if $\\beta \\rho \\gtrsim 1$."}],"day":"08","author":[{"last_name":"Deuchert","first_name":"Andreas","full_name":"Deuchert, Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Simon","last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","full_name":"Mayer, Simon"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer"}],"page":"61","scopus_import":1,"ec_funded":1,"article_processing_charge":"No","_id":"7524","publication":"arXiv:1910.03372","department":[{"_id":"RoSe"}],"year":"2019","publisher":"ArXiv","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"publication_status":"published","oa":1,"date_published":"2018-12-12T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01204"}],"status":"public","external_id":{"isi":["000452992700008"],"arxiv":["1809.01204"]},"intvolume":"        98","citation":{"short":"E. Yakaboylu, B. Midya, A. Deuchert, N.K. Leopold, M. Lemeshko, Physical Review B 98 (2018).","chicago":"Yakaboylu, Enderalp, Bikashkali Midya, Andreas Deuchert, Nikolai K Leopold, and Mikhail Lemeshko. “Theory of the Rotating Polaron: Spectrum and Self-Localization.” <i>Physical Review B</i>. American Physical Society, 2018. <a href=\"https://doi.org/10.1103/physrevb.98.224506\">https://doi.org/10.1103/physrevb.98.224506</a>.","ieee":"E. Yakaboylu, B. Midya, A. Deuchert, N. K. Leopold, and M. Lemeshko, “Theory of the rotating polaron: Spectrum and self-localization,” <i>Physical Review B</i>, vol. 98, no. 22. American Physical Society, 2018.","apa":"Yakaboylu, E., Midya, B., Deuchert, A., Leopold, N. K., &#38; Lemeshko, M. (2018). Theory of the rotating polaron: Spectrum and self-localization. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevb.98.224506\">https://doi.org/10.1103/physrevb.98.224506</a>","ista":"Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. 2018. Theory of the rotating polaron: Spectrum and self-localization. Physical Review B. 98(22), 224506.","mla":"Yakaboylu, Enderalp, et al. “Theory of the Rotating Polaron: Spectrum and Self-Localization.” <i>Physical Review B</i>, vol. 98, no. 22, 224506, American Physical Society, 2018, doi:<a href=\"https://doi.org/10.1103/physrevb.98.224506\">10.1103/physrevb.98.224506</a>.","ama":"Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. Theory of the rotating polaron: Spectrum and self-localization. <i>Physical Review B</i>. 2018;98(22). doi:<a href=\"https://doi.org/10.1103/physrevb.98.224506\">10.1103/physrevb.98.224506</a>"},"abstract":[{"text":"We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a “rotating polaron,” which can be used to model, e.g., a rotating molecule immersed in an ultracold Bose gas or superfluid helium. We derive the Hamiltonian of the rotating polaron and study its spectrum in the weak- and strong-coupling regimes using a combination of variational, diagrammatic, and mean-field approaches. We reveal how the coupling between linear and angular momenta affects stable quasiparticle states, and demonstrate that internal rotation leads to an enhanced self-localization in the translational degrees of freedom.","lang":"eng"}],"date_updated":"2023-09-19T14:29:03Z","type":"journal_article","oa_version":"Preprint","month":"12","volume":98,"date_created":"2019-02-14T10:37:09Z","year":"2018","_id":"5983","publication_identifier":{"issn":["2469-9950"],"eissn":["2469-9969"]},"doi":"10.1103/physrevb.98.224506","quality_controlled":"1","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"},{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"isi":1,"language":[{"iso":"eng"}],"issue":"22","author":[{"first_name":"Enderalp","last_name":"Yakaboylu","full_name":"Yakaboylu, Enderalp","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5973-0874"},{"full_name":"Midya, Bikashkali","id":"456187FC-F248-11E8-B48F-1D18A9856A87","first_name":"Bikashkali","last_name":"Midya"},{"last_name":"Deuchert","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas"},{"orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K","last_name":"Leopold","first_name":"Nikolai K"},{"last_name":"Lemeshko","first_name":"Mikhail","orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Lemeshko, Mikhail"}],"day":"12","title":"Theory of the rotating polaron: Spectrum and self-localization","arxiv":1,"article_number":"224506","publisher":"American Physical Society","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"publication":"Physical Review B","article_processing_charge":"No","ec_funded":1,"scopus_import":"1"},{"year":"2018","_id":"400","page":"1507 - 1527","abstract":[{"text":"We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. In the case of vanishing angular momentum, our results carry over to the three-dimensional case.","lang":"eng"}],"date_updated":"2023-09-15T12:04:15Z","month":"05","type":"journal_article","oa_version":"Published Version","volume":19,"date_created":"2018-12-11T11:46:15Z","file_date_updated":"2020-07-14T12:46:22Z","status":"public","external_id":{"isi":["000429799900008"]},"intvolume":"        19","citation":{"short":"A. Deuchert, A. Geisinge, C. Hainzl, M. Loss, Annales Henri Poincare 19 (2018) 1507–1527.","ieee":"A. Deuchert, A. Geisinge, C. Hainzl, and M. Loss, “Persistence of translational symmetry in the BCS model with radial pair interaction,” <i>Annales Henri Poincare</i>, vol. 19, no. 5. Springer, pp. 1507–1527, 2018.","chicago":"Deuchert, Andreas, Alissa Geisinge, Christian Hainzl, and Michael Loss. “Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction.” <i>Annales Henri Poincare</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00023-018-0665-7\">https://doi.org/10.1007/s00023-018-0665-7</a>.","mla":"Deuchert, Andreas, et al. “Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction.” <i>Annales Henri Poincare</i>, vol. 19, no. 5, Springer, 2018, pp. 1507–27, doi:<a href=\"https://doi.org/10.1007/s00023-018-0665-7\">10.1007/s00023-018-0665-7</a>.","ista":"Deuchert A, Geisinge A, Hainzl C, Loss M. 2018. Persistence of translational symmetry in the BCS model with radial pair interaction. Annales Henri Poincare. 19(5), 1507–1527.","apa":"Deuchert, A., Geisinge, A., Hainzl, C., &#38; Loss, M. (2018). Persistence of translational symmetry in the BCS model with radial pair interaction. <i>Annales Henri Poincare</i>. Springer. <a href=\"https://doi.org/10.1007/s00023-018-0665-7\">https://doi.org/10.1007/s00023-018-0665-7</a>","ama":"Deuchert A, Geisinge A, Hainzl C, Loss M. Persistence of translational symmetry in the BCS model with radial pair interaction. <i>Annales Henri Poincare</i>. 2018;19(5):1507-1527. doi:<a href=\"https://doi.org/10.1007/s00023-018-0665-7\">10.1007/s00023-018-0665-7</a>"},"publication_status":"published","oa":1,"has_accepted_license":"1","date_published":"2018-05-01T00:00:00Z","ddc":["510"],"publisher":"Springer","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"RoSe"}],"publication":"Annales Henri Poincare","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"scopus_import":"1","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)"},"author":[{"last_name":"Deuchert","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas"},{"full_name":"Geisinge, Alissa","first_name":"Alissa","last_name":"Geisinge"},{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"full_name":"Loss, Michael","first_name":"Michael","last_name":"Loss"}],"file":[{"access_level":"open_access","date_created":"2018-12-12T10:12:47Z","checksum":"04d2c9bd7cbf3ca1d7acaaf4e7dca3e5","date_updated":"2020-07-14T12:46:22Z","file_id":"4966","creator":"system","content_type":"application/pdf","relation":"main_file","file_size":582680,"file_name":"IST-2018-1011-v1+1_2018_Deuchert_Persistence.pdf"}],"day":"01","title":"Persistence of translational symmetry in the BCS model with radial pair interaction","publist_id":"7429","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"isi":1,"language":[{"iso":"eng"}],"issue":"5","pubrep_id":"1011","doi":"10.1007/s00023-018-0665-7","quality_controlled":"1"},{"article_number":"081901","title":"A lower bound for the BCS functional with boundary conditions at infinity","publist_id":"6531","author":[{"full_name":"Deuchert, Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert","first_name":"Andreas"}],"day":"01","publication":" Journal of Mathematical Physics","scopus_import":"1","ec_funded":1,"article_processing_charge":"No","publisher":"AIP Publishing","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"doi":"10.1063/1.4996580","quality_controlled":"1","publication_identifier":{"issn":["00222488"]},"isi":1,"issue":"8","language":[{"iso":"eng"}],"project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"volume":58,"date_created":"2018-12-11T11:49:10Z","oa_version":"Submitted Version","type":"journal_article","month":"08","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"}],"date_updated":"2024-02-28T13:07:56Z","_id":"912","year":"2017","date_published":"2017-08-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.04616"}],"publication_status":"published","oa":1,"intvolume":"        58","citation":{"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>","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>.","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>","short":"A. Deuchert,  Journal of Mathematical Physics 58 (2017).","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>.","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."},"status":"public","external_id":{"isi":["000409197200015"]}},{"isi":1,"issue":"23","language":[{"iso":"eng"}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"grant_number":"P29902","call_identifier":"FWF","_id":"26031614-B435-11E9-9278-68D0E5697425","name":"Quantum rotations in the presence of a many-body environment"}],"doi":"10.1103/PhysRevLett.119.235301","quality_controlled":"1","publication_identifier":{"issn":["0031-9007"]},"publication":"Physical Review Letters","article_type":"original","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"article_number":"235301","title":"Emergence of non-abelian magnetic monopoles in a quantum impurity problem","arxiv":1,"publist_id":"6401","author":[{"first_name":"Enderalp","last_name":"Yakaboylu","orcid":"0000-0001-5973-0874","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","full_name":"Yakaboylu, Enderalp"},{"first_name":"Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746","full_name":"Deuchert, Andreas"},{"full_name":"Lemeshko, Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802","last_name":"Lemeshko","first_name":"Mikhail"}],"day":"06","intvolume":"       119","citation":{"ieee":"E. Yakaboylu, A. Deuchert, and M. Lemeshko, “Emergence of non-abelian magnetic monopoles in a quantum impurity problem,” <i>Physical Review Letters</i>, vol. 119, no. 23. American Physical Society, 2017.","chicago":"Yakaboylu, Enderalp, Andreas Deuchert, and Mikhail Lemeshko. “Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.” <i>Physical Review Letters</i>. American Physical Society, 2017. <a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">https://doi.org/10.1103/PhysRevLett.119.235301</a>.","short":"E. Yakaboylu, A. Deuchert, M. Lemeshko, Physical Review Letters 119 (2017).","ama":"Yakaboylu E, Deuchert A, Lemeshko M. Emergence of non-abelian magnetic monopoles in a quantum impurity problem. <i>Physical Review Letters</i>. 2017;119(23). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">10.1103/PhysRevLett.119.235301</a>","mla":"Yakaboylu, Enderalp, et al. “Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.” <i>Physical Review Letters</i>, vol. 119, no. 23, 235301, American Physical Society, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">10.1103/PhysRevLett.119.235301</a>.","ista":"Yakaboylu E, Deuchert A, Lemeshko M. 2017. Emergence of non-abelian magnetic monopoles in a quantum impurity problem. Physical Review Letters. 119(23), 235301.","apa":"Yakaboylu, E., Deuchert, A., &#38; Lemeshko, M. (2017). Emergence of non-abelian magnetic monopoles in a quantum impurity problem. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.119.235301\">https://doi.org/10.1103/PhysRevLett.119.235301</a>"},"status":"public","external_id":{"isi":["000417132100007"],"arxiv":["1705.05162"]},"date_published":"2017-12-06T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1705.05162","open_access":"1"}],"oa":1,"publication_status":"published","_id":"997","year":"2017","volume":119,"date_created":"2018-12-11T11:49:36Z","month":"12","type":"journal_article","oa_version":"Preprint","abstract":[{"text":"Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.","lang":"eng"}],"date_updated":"2023-10-10T13:31:54Z"}]