{"title":"Polarons in Bose gases and polar crystals: Some rigorous energy estimates","article_processing_charge":"No","publication_identifier":{"issn":["2663-337X"]},"file_date_updated":"2022-07-05T08:17:12Z","degree_awarded":"PhD","language":[{"iso":"eng"}],"date_created":"2022-06-30T12:15:03Z","project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"acknowledged_ssus":[{"_id":"SSU"}],"page":"138","day":"01","file":[{"content_type":"application/pdf","file_name":"thes1_no_isbn_2_1b.pdf","relation":"main_file","creator":"kmysliwy","checksum":"7970714a20a6052f75fb27a6c3e9976e","date_updated":"2022-07-05T08:12:56Z","file_size":1830973,"date_created":"2022-07-05T08:12:56Z","success":1,"access_level":"open_access","file_id":"11486"},{"file_name":"thes_source.zip","relation":"source_file","content_type":"application/zip","date_updated":"2022-07-05T08:17:12Z","file_size":5831060,"date_created":"2022-07-05T08:15:52Z","creator":"kmysliwy","checksum":"647a2011fdf56277096c9350fefe1097","access_level":"closed","file_id":"11487"}],"publisher":"Institute of Science and Technology Austria","type":"dissertation","supervisor":[{"full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"abstract":[{"lang":"eng","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"}],"ec_funded":1,"oa":1,"oa_version":"Published Version","date_published":"2022-07-01T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"id":"316457FC-F248-11E8-B48F-1D18A9856A87","last_name":"Mysliwy","first_name":"Krzysztof","full_name":"Mysliwy, Krzysztof"}],"has_accepted_license":"1","date_updated":"2023-09-07T13:43:52Z","doi":"10.15479/at:ista:11473","alternative_title":["ISTA Thesis"],"_id":"11473","year":"2022","ddc":["515","539"],"citation":{"apa":"Mysliwy, K. (2022). <i>Polarons in Bose gases and polar crystals: Some rigorous energy estimates</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:11473\">https://doi.org/10.15479/at:ista:11473</a>","ama":"Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. 2022. doi:<a href=\"https://doi.org/10.15479/at:ista:11473\">10.15479/at:ista:11473</a>","chicago":"Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates.” Institute of Science and Technology Austria, 2022. <a href=\"https://doi.org/10.15479/at:ista:11473\">https://doi.org/10.15479/at:ista:11473</a>.","short":"K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates, Institute of Science and Technology Austria, 2022.","ieee":"K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy estimates,” Institute of Science and Technology Austria, 2022.","ista":"Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria.","mla":"Mysliwy, Krzysztof. <i>Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates</i>. Institute of Science and Technology Austria, 2022, doi:<a href=\"https://doi.org/10.15479/at:ista:11473\">10.15479/at:ista:11473</a>."},"month":"07","publication_status":"published","status":"public","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10564"},{"relation":"part_of_dissertation","status":"public","id":"8705"}]}}