{"title":"Existence of Ground States in the Infrared-Critial Spin Boson Model","conference":{"start_date":"2021-12-06","location":"RIMS, Kyoto","name":"Mathematical aspects of quantum fields and related topics","end_date":"2021-12-08"},"abstract":[{"lang":"eng","text":"We review recent results on the existence of ground states for the\r\ninfrared-critical spin boson model, which describes the interaction of a\r\nmassless bosonic field with a two-state quantum system. Explicitly, we derive a\r\ncritical coupling $\\lambda_{\\mathsf c}>0$ such that the spin boson model\r\nexhibits a ground state for coupling constants $\\lambda$ with\r\n$|\\lambda|<\\lambda_{\\mathsf c}$. The proof combines a Feynman-Kac-Nelson\r\nformula for the spin boson model with external magnetic field, a 1D-Ising model\r\ncorrelation bound and a compactness argument in Fock space. Elaborating on the\r\nconnection to a long-range 1D-Ising model, we briefly discuss the conjecture\r\nthat the spin boson model does not have a ground state at large coupling. This\r\nnote is based on joint work with David Hasler and Oliver Siebert."}],"extern":"1","intvolume":"      2235","series_title":"RIMS Kôkyûroku","date_updated":"2023-06-13T10:13:31Z","volume":2235,"date_created":"2023-04-14T04:56:51Z","external_id":{"arxiv":["2204.00287"]},"publication_status":"published","author":[{"full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","id":"99427","first_name":"Benjamin","orcid":"0000-0001-9074-1205"}],"main_file_link":[{"url":"http://hdl.handle.net/2433/282934"}],"editor":[{"full_name":"Hiroshima, Fumio","last_name":"Hiroshima","first_name":"Fumio"}],"publication":"Mathematical aspects of quantum fields and related topics","language":[{"iso":"eng"}],"page":"60-73","type":"conference","citation":{"apa":"Hinrichs, B. (2022). Existence of Ground States in the Infrared-Critial Spin Boson Model. In F. Hiroshima (Ed.), <i>Mathematical aspects of quantum fields and related topics</i> (Vol. 2235, pp. 60–73).","chicago":"Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin Boson Model.” In <i>Mathematical Aspects of Quantum Fields and Related Topics</i>, edited by Fumio Hiroshima, 2235:60–73. RIMS Kôkyûroku, 2022.","mla":"Hinrichs, Benjamin. “Existence of Ground States in the Infrared-Critial Spin Boson Model.” <i>Mathematical Aspects of Quantum Fields and Related Topics</i>, edited by Fumio Hiroshima, vol. 2235, 2022, pp. 60–73.","ieee":"B. Hinrichs, “Existence of Ground States in the Infrared-Critial Spin Boson Model,” in <i>Mathematical aspects of quantum fields and related topics</i>, RIMS, Kyoto, 2022, vol. 2235, pp. 60–73.","bibtex":"@inproceedings{Hinrichs_2022, series={RIMS Kôkyûroku}, title={Existence of Ground States in the Infrared-Critial Spin Boson Model}, volume={2235}, booktitle={Mathematical aspects of quantum fields and related topics}, author={Hinrichs, Benjamin}, editor={Hiroshima, Fumio}, year={2022}, pages={60–73}, collection={RIMS Kôkyûroku} }","ama":"Hinrichs B. Existence of Ground States in the Infrared-Critial Spin Boson Model. In: Hiroshima F, ed. <i>Mathematical Aspects of Quantum Fields and Related Topics</i>. Vol 2235. RIMS Kôkyûroku. ; 2022:60-73.","short":"B. Hinrichs, in: F. Hiroshima (Ed.), Mathematical Aspects of Quantum Fields and Related Topics, 2022, pp. 60–73."},"_id":"43496","status":"public","year":"2022","user_id":"99427"}