[{"_id":"12246","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","type":"journal_article","article_type":"original","date_updated":"2023-09-05T15:17:34Z","department":[{"_id":"RoSe"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy."}],"intvolume":" 112","month":"09","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2203.12473"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"ec_funded":1,"issue":"5","volume":112,"article_number":"92","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92.","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5.","apa":"Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-022-01584-5","ama":"Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5","short":"M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the indirect and exchange energies,” Letters in Mathematical Physics, vol. 112, no. 5. Springer Nature, 2022.","mla":"Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer Nature, 2022, doi:10.1007/s11005-022-01584-5."},"title":"Improved Lieb–Oxford bound on the indirect and exchange energies","article_processing_charge":"No","external_id":{"isi":["000854762600001"],"arxiv":["2203.12473"]},"author":[{"full_name":"Lewin, Mathieu","last_name":"Lewin","first_name":"Mathieu"},{"last_name":"Lieb","full_name":"Lieb, Elliott H.","first_name":"Elliott H."},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"acknowledgement":"We would like to thank David Gontier for useful advice on the numerical simulations. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful for the hospitality of the Institut Henri Poincaré in Paris, where part of this work was done.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","publication":"Letters in Mathematical Physics","day":"15","year":"2022","isi":1,"date_created":"2023-01-16T09:53:54Z","date_published":"2022-09-15T00:00:00Z","doi":"10.1007/s11005-022-01584-5"},{"file":[{"success":1,"file_id":"11486","checksum":"7970714a20a6052f75fb27a6c3e9976e","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"thes1_no_isbn_2_1b.pdf","date_created":"2022-07-05T08:12:56Z","creator":"kmysliwy","file_size":1830973,"date_updated":"2022-07-05T08:12:56Z"},{"checksum":"647a2011fdf56277096c9350fefe1097","file_id":"11487","access_level":"closed","relation":"source_file","content_type":"application/zip","date_created":"2022-07-05T08:15:52Z","file_name":"thes_source.zip","creator":"kmysliwy","date_updated":"2022-07-05T08:17:12Z","file_size":5831060}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10564"},{"id":"8705","status":"public","relation":"part_of_dissertation"}]},"ec_funded":1,"oa_version":"Published Version","acknowledged_ssus":[{"_id":"SSU"}],"abstract":[{"text":"The polaron model is a basic model of quantum field theory describing a single particle\r\ninteracting with a bosonic field. It arises in many physical contexts. We are mostly concerned\r\nwith models applicable in the context of an impurity atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving in polar crystals.\r\nThe model has a simple structure in which the interaction of the particle with the field is given\r\nby a term linear in the field’s creation and annihilation operators. In this work, we investigate\r\nthe properties of this model by providing rigorous estimates on various energies relevant to the\r\nproblem. The estimates are obtained, for the most part, by suitable operator techniques which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe first application of these techniques is to derive the polaron model rigorously from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective theory for this problem.\r\nIn the second part, we investigate rigorously the ground state of the model at fixed momentum\r\nand for large values of the coupling constant. Qualitatively, the system is expected to display\r\na transition from the quasi-particle behavior at small momenta, where the dispersion relation\r\nis parabolic and the particle moves through the medium dragging along a cloud of phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates and emits free phonons.\r\nAt the same time, in the strong coupling regime, the bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst studied by Landau and Pekar in the 1940s. For polaron models with regularized form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in the interacting Bose gas, we prove\r\nthat for a large window of momenta below the radiation threshold, the energy-momentum\r\nrelation at strong coupling is indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons in polar crystals where the dispersion relation is\r\nof the optical type and the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe regular case, this requires the inclusion of the quantum fluctuations of the phonon field,\r\nwhich makes the problem considerably more difficult.\r\nThe results are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na proof of the divergence of the effective mass with the coupling constant for a wide class of\r\npolaron models, as well as the discussion of the apparent UV singularity of the Fröhlich model\r\nand the application of the techniques used for its removal for the energy estimates.\r\n","lang":"eng"}],"month":"07","alternative_title":["ISTA Thesis"],"ddc":["515","539"],"supervisor":[{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"date_updated":"2023-09-07T13:43:52Z","file_date_updated":"2022-07-05T08:17:12Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"_id":"11473","status":"public","type":"dissertation","day":"01","has_accepted_license":"1","year":"2022","doi":"10.15479/at:ista:11473","date_published":"2022-07-01T00:00:00Z","date_created":"2022-06-30T12:15:03Z","page":"138","publisher":"Institute of Science and Technology Austria","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria.","chicago":"Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:11473.","ieee":"K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy estimates,” Institute of Science and Technology Austria, 2022.","short":"K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates, Institute of Science and Technology Austria, 2022.","apa":"Mysliwy, K. (2022). Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:11473","ama":"Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. 2022. doi:10.15479/at:ista:11473","mla":"Mysliwy, Krzysztof. Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:11473."},"title":"Polarons in Bose gases and polar crystals: Some rigorous energy estimates","author":[{"full_name":"Mysliwy, Krzysztof","last_name":"Mysliwy","first_name":"Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"}]},{"intvolume":" 186","month":"01","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.","lang":"eng"}],"ec_funded":1,"volume":186,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"11473"}]},"issue":"1","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"10716","checksum":"da03f6d293c4b9802091bce9471b1d29","success":1,"date_updated":"2022-02-02T14:24:41Z","file_size":434957,"creator":"cchlebak","date_created":"2022-02-02T14:24:41Z","file_name":"2022_JournalStatPhys_Myśliwy.pdf"}],"publication_status":"published","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"status":"public","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)"},"type":"journal_article","article_type":"original","_id":"10564","file_date_updated":"2022-02-02T14:24:41Z","department":[{"_id":"RoSe"}],"ddc":["530"],"date_updated":"2023-09-07T13:43:51Z","oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"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.) and the Maria Skłodowska-Curie Grant Agreement No. 665386 (K.M.) is gratefully acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","date_created":"2021-12-19T23:01:32Z","date_published":"2022-01-01T00:00:00Z","doi":"10.1007/s10955-021-02851-w","publication":"Journal of Statistical Physics","day":"01","year":"2022","has_accepted_license":"1","isi":1,"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_number":"5","title":"Polaron models with regular interactions at strong coupling","external_id":{"isi":["000726275600001"],"arxiv":["2106.09328"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Mysliwy, Krzysztof","last_name":"Mysliwy","first_name":"Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ama":"Mysliwy K, Seiringer R. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w","apa":"Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w","ieee":"K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer Nature, 2022.","short":"K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022).","mla":"Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5, Springer Nature, 2022, doi:10.1007/s10955-021-02851-w.","ista":"Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 186(1), 5.","chicago":"Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w."}},{"_id":"10850","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","keyword":["Analysis"],"date_updated":"2023-10-27T10:37:29Z","ddc":["510"],"file_date_updated":"2022-08-02T10:37:55Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"abstract":[{"text":"We study two interacting quantum particles forming a bound state in d-dimensional free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly decreases upon going from k\r\nto k+1. This shows that the particles stick to the corner where all boundary planes intersect.\r\nSecond, we show that for all k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020) to dimensions d > 1.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"06","intvolume":" 282","publication_identifier":{"issn":["0022-1236"]},"publication_status":"published","file":[{"file_size":631391,"date_updated":"2022-08-02T10:37:55Z","creator":"dernst","file_name":"2022_JourFunctionalAnalysis_Roos.pdf","date_created":"2022-08-02T10:37:55Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"11720","checksum":"63efcefaa1f2717244ef5407bd564426"}],"language":[{"iso":"eng"}],"issue":"12","volume":282,"related_material":{"record":[{"id":"14374","status":"public","relation":"dissertation_contains"}]},"ec_funded":1,"article_number":"109455","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"citation":{"mla":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455, Elsevier, 2022, doi:10.1016/j.jfa.2022.109455.","apa":"Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455","ama":"Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455","short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).","ieee":"B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022.","chicago":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455.","ista":"Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Roos","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","first_name":"Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000795160200009"],"arxiv":["2105.04874"]},"title":"Two-particle bound states at interfaces and corners","acknowledgement":"We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged.","publisher":"Elsevier","quality_controlled":"1","oa":1,"isi":1,"has_accepted_license":"1","year":"2022","day":"15","publication":"Journal of Functional Analysis","doi":"10.1016/j.jfa.2022.109455","date_published":"2022-06-15T00:00:00Z","date_created":"2022-03-16T08:41:53Z"},{"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","_id":"10755","file_date_updated":"2022-02-14T08:20:19Z","department":[{"_id":"RoSe"}],"date_updated":"2024-03-06T12:30:44Z","ddc":["510"],"scopus_import":"1","month":"01","intvolume":" 55","abstract":[{"lang":"eng","text":"We provide a definition of the effective mass for the classical polaron described by the Landau–Pekar (LP) equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by LP (1948 J. Exp. Theor. Phys. 18 419–423)."}],"oa_version":"Published Version","volume":55,"issue":"1","related_material":{"record":[{"status":"public","id":"9791","relation":"earlier_version"}]},"ec_funded":1,"publication_identifier":{"eissn":["1751-8121"],"issn":["1751-8113"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"10757","checksum":"0875e562705563053d6dd98fba4d8578","file_size":1132380,"date_updated":"2022-02-14T08:20:19Z","creator":"dernst","file_name":"2022_JournalPhysicsA_Feliciangeli.pdf","date_created":"2022-02-14T08:20:19Z"}],"language":[{"iso":"eng"}],"project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"015201","author":[{"last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466","last_name":"Rademacher"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2107.03720"]},"title":"The effective mass problem for the Landau-Pekar equations","citation":{"ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1. IOP Publishing, 2022.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A: Mathematical and Theoretical 55 (2022).","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 2022;55(1). doi:10.1088/1751-8121/ac3947","apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2022). The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/ac3947","mla":"Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1, 015201, IOP Publishing, 2022, doi:10.1088/1751-8121/ac3947.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 55(1), 015201.","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2022. https://doi.org/10.1088/1751-8121/ac3947."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"IOP Publishing","quality_controlled":"1","oa":1,"acknowledgement":"We thank Herbert Spohn for helpful comments. Funding from the European Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (SR) is\r\ngratefully acknowledged.","date_published":"2022-01-19T00:00:00Z","doi":"10.1088/1751-8121/ac3947","date_created":"2022-02-13T23:01:35Z","has_accepted_license":"1","year":"2022","day":"19","publication":"Journal of Physics A: Mathematical and Theoretical"},{"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle"}],"month":"12","intvolume":" 9","scopus_import":"1","file":[{"date_created":"2022-01-03T10:15:05Z","file_name":"2021_Atoms_Brooks.pdf","creator":"alisjak","date_updated":"2022-01-03T10:15:05Z","file_size":303070,"checksum":"d0e44b95f36c9e06724f66832af0f8c3","file_id":"10592","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2218-2004"]},"publication_status":"published","volume":9,"issue":"4","_id":"10585","status":"public","keyword":["anyons","quasiparticles","Quantum Hall Effect","topological states of matter"],"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)"},"ddc":["530"],"date_updated":"2023-06-15T14:51:49Z","file_date_updated":"2022-01-03T10:15:05Z","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"acknowledgement":"D. Lundholm acknowledges financial support from the Göran Gustafsson Foundation (grant no. 1804).","publisher":"MDPI","quality_controlled":"1","oa":1,"day":"02","publication":"Atoms","has_accepted_license":"1","year":"2021","doi":"10.3390/atoms9040106","date_published":"2021-12-02T00:00:00Z","date_created":"2022-01-02T23:01:33Z","article_number":"106","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"short":"M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Atoms 9 (2021).","ieee":"M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Emergence of anyons on the two-sphere in molecular impurities,” Atoms, vol. 9, no. 4. MDPI, 2021.","apa":"Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Emergence of anyons on the two-sphere in molecular impurities. Atoms. MDPI. https://doi.org/10.3390/atoms9040106","ama":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 2021;9(4). doi:10.3390/atoms9040106","mla":"Brooks, Morris, et al. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” Atoms, vol. 9, no. 4, 106, MDPI, 2021, doi:10.3390/atoms9040106.","ista":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 9(4), 106.","chicago":"Brooks, Morris, Mikhail Lemeshko, Douglas Lundholm, and Enderalp Yakaboylu. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” Atoms. MDPI, 2021. https://doi.org/10.3390/atoms9040106."},"title":"Emergence of anyons on the two-sphere in molecular impurities","author":[{"first_name":"Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","orcid":"0000-0002-6249-0928","full_name":"Brooks, Morris","last_name":"Brooks"},{"id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","full_name":"Lemeshko, Mikhail","orcid":"0000-0002-6990-7802","last_name":"Lemeshko"},{"last_name":"Lundholm","full_name":"Lundholm, Douglas","first_name":"Douglas"},{"orcid":"0000-0001-5973-0874","full_name":"Yakaboylu, Enderalp","last_name":"Yakaboylu","first_name":"Enderalp","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["2108.06966"]},"article_processing_charge":"Yes"},{"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"article_number":"2060006","author":[{"id":"342E7E22-F248-11E8-B48F-1D18A9856A87","first_name":"Chiara","full_name":"Boccato, Chiara","last_name":"Boccato"}],"article_processing_charge":"No","external_id":{"arxiv":["2001.00497"],"isi":["000613313200007"]},"title":"The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime","citation":{"mla":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” Reviews in Mathematical Physics, vol. 33, no. 1, 2060006, World Scientific, 2021, doi:10.1142/S0129055X20600065.","short":"C. Boccato, Reviews in Mathematical Physics 33 (2021).","ieee":"C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime,” Reviews in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021.","ama":"Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 2021;33(1). doi:10.1142/S0129055X20600065","apa":"Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. World Scientific. https://doi.org/10.1142/S0129055X20600065","chicago":"Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” Reviews in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/S0129055X20600065.","ista":"Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 33(1), 2060006."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"World Scientific","quality_controlled":"1","oa":1,"doi":"10.1142/S0129055X20600065","date_published":"2021-01-01T00:00:00Z","date_created":"2020-04-26T22:00:45Z","isi":1,"year":"2021","day":"01","publication":"Reviews in Mathematical Physics","type":"journal_article","article_type":"original","status":"public","_id":"7685","department":[{"_id":"RoSe"}],"date_updated":"2023-08-04T10:50:13Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.00497"}],"month":"01","intvolume":" 33","abstract":[{"lang":"eng","text":"We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein."}],"oa_version":"Preprint","volume":33,"issue":"1","ec_funded":1,"publication_identifier":{"issn":["0129-055X"]},"publication_status":"published","language":[{"iso":"eng"}]},{"acknowledgement":"Partial support through National Science Foundation GrantDMS-1363432 (R.L.F.) and the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo 694227; R.S.), is acknowledged. Open access funding enabled and organizedby Projekt DEAL.","publisher":"Wiley","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Communications on Pure and Applied Mathematics","page":"544-588","doi":"10.1002/cpa.21944","date_published":"2021-03-01T00:00:00Z","date_created":"2020-10-04T22:01:37Z","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"mla":"Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron.” Communications on Pure and Applied Mathematics, vol. 74, no. 3, Wiley, 2021, pp. 544–88, doi:10.1002/cpa.21944.","apa":"Frank, R., & Seiringer, R. (2021). Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21944","ama":"Frank R, Seiringer R. Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. 2021;74(3):544-588. doi:10.1002/cpa.21944","ieee":"R. Frank and R. Seiringer, “Quantum corrections to the Pekar asymptotics of a strongly coupled polaron,” Communications on Pure and Applied Mathematics, vol. 74, no. 3. Wiley, pp. 544–588, 2021.","short":"R. Frank, R. Seiringer, Communications on Pure and Applied Mathematics 74 (2021) 544–588.","chicago":"Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron.” Communications on Pure and Applied Mathematics. Wiley, 2021. https://doi.org/10.1002/cpa.21944.","ista":"Frank R, Seiringer R. 2021. Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. 74(3), 544–588."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Rupert","full_name":"Frank, Rupert","last_name":"Frank"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"article_processing_charge":"No","external_id":{"isi":["000572991500001"]},"title":"Quantum corrections to the Pekar asymptotics of a strongly coupled polaron","abstract":[{"lang":"eng","text":"We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem."}],"oa_version":"Published Version","scopus_import":"1","month":"03","intvolume":" 74","publication_identifier":{"eissn":["10970312"],"issn":["00103640"]},"publication_status":"published","file":[{"checksum":"5f665ffa6e6dd958aec5c3040cbcfa84","file_id":"9236","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2021-03-11T10:03:30Z","file_name":"2021_CommPureApplMath_Frank.pdf","creator":"dernst","date_updated":"2021-03-11T10:03:30Z","file_size":334987}],"language":[{"iso":"eng"}],"volume":74,"issue":"3","ec_funded":1,"_id":"8603","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":"2023-08-04T11:02:16Z","ddc":["510"],"file_date_updated":"2021-03-11T10:03:30Z","department":[{"_id":"RoSe"}]},{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field."}],"intvolume":" 126","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2009.05948"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00319007"],"eissn":["10797114"]},"ec_funded":1,"related_material":{"link":[{"relation":"press_release","url":"https://ist.ac.at/en/news/dancing-molecules-and-two-dimensional-particles/","description":"News on IST Homepage"}],"record":[{"status":"public","id":"12390","relation":"dissertation_contains"}]},"volume":126,"issue":"1","_id":"9005","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-08-07T13:32:10Z","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"acknowledgement":"We are grateful to A. Ghazaryan for valuable discussions and also thank the anonymous referees for comments. D.L. acknowledges financial support from the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully acknowledges financial support\r\nby the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 801770).","oa":1,"publisher":"American Physical Society","quality_controlled":"1","publication":"Physical Review Letters","day":"08","year":"2021","isi":1,"date_created":"2021-01-17T23:01:10Z","doi":"10.1103/PhysRevLett.126.015301","date_published":"2021-01-08T00:00:00Z","article_number":"015301","project":[{"call_identifier":"H2020","_id":"2688CF98-B435-11E9-9278-68D0E5697425","grant_number":"801770","name":"Angulon: physics and applications of a new quasiparticle"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ama":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 2021;126(1). doi:10.1103/PhysRevLett.126.015301","apa":"Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.126.015301","short":"M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Physical Review Letters 126 (2021).","ieee":"M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities as a realization of anyons on the two-sphere,” Physical Review Letters, vol. 126, no. 1. American Physical Society, 2021.","mla":"Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters, vol. 126, no. 1, 015301, American Physical Society, 2021, doi:10.1103/PhysRevLett.126.015301.","ista":"Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 126(1), 015301.","chicago":"Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters. American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.015301."},"title":"Molecular impurities as a realization of anyons on the two-sphere","external_id":{"arxiv":["2009.05948"],"isi":["000606325000003"]},"article_processing_charge":"No","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","first_name":"Morris","last_name":"Brooks","full_name":"Brooks, Morris","orcid":"0000-0002-6249-0928"},{"id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","last_name":"Lemeshko","full_name":"Lemeshko, Mikhail","orcid":"0000-0002-6990-7802"},{"full_name":"Lundholm, D.","last_name":"Lundholm","first_name":"D."},{"orcid":"0000-0001-5973-0874","full_name":"Yakaboylu, Enderalp","last_name":"Yakaboylu","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","first_name":"Enderalp"}]},{"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"citation":{"chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01616-9.","ista":"Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.","mla":"Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis, vol. 240, Springer Nature, 2021, pp. 383–417, doi:10.1007/s00205-021-01616-9.","ieee":"N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” Archive for Rational Mechanics and Analysis, vol. 240. Springer Nature, pp. 383–417, 2021.","short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417.","ama":"Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 2021;240:383-417. doi:10.1007/s00205-021-01616-9","apa":"Leopold, N. K., Mitrouskas, D. J., & Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01616-9"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000622226200001"],"arxiv":["2001.03993"]},"author":[{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","first_name":"Nikolai K","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","last_name":"Leopold"},{"last_name":"Mitrouskas","full_name":"Mitrouskas, David Johannes","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","acknowledgement":"Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","year":"2021","has_accepted_license":"1","isi":1,"publication":"Archive for Rational Mechanics and Analysis","day":"26","page":"383-417","date_created":"2021-03-14T23:01:34Z","date_published":"2021-02-26T00:00:00Z","doi":"10.1007/s00205-021-01616-9","_id":"9246","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)"},"type":"journal_article","article_type":"original","status":"public","date_updated":"2023-08-07T14:12:27Z","ddc":["510"],"department":[{"_id":"RoSe"}],"file_date_updated":"2021-03-22T08:31:29Z","abstract":[{"lang":"eng","text":"We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 240","month":"02","publication_status":"published","publication_identifier":{"issn":["00039527"],"eissn":["14320673"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":558006,"date_updated":"2021-03-22T08:31:29Z","file_name":"2021_ArchRationalMechAnal_Leopold.pdf","date_created":"2021-03-22T08:31:29Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"9270","checksum":"23449e44dc5132501a5c86e70638800f"}],"ec_funded":1,"volume":240}]