{"title":"Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains","publication":"arXiv:2403.12147","abstract":[{"text":"We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics. The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical electrons moving in a polarizable crystal and interacting with the\r\nquantized phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We also include possibly very singular magnetic vector potentials and\r\nelectrostatic potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative functionals and can be applied to every vector\r\nin the underlying Hilbert space. In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac formulas are known, the analysis of the\r\ncreation and annihilation terms in the multiplicative functionals requires\r\nnovel ideas to overcome difficulties caused by the phonon dispersion relation\r\nbeing constant. Getting these terms under control and generalizing other\r\nconstruction steps so as to cover confined systems are the main achievements of\r\nthis article.","lang":"eng"}],"language":[{"iso":"eng"}],"date_updated":"2024-03-20T14:56:50Z","type":"preprint","citation":{"apa":"Hinrichs, B., &#38; Matte, O. (2024). Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains. In <i>arXiv:2403.12147</i>.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.” <i>ArXiv:2403.12147</i>, 2024.","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.” <i>ArXiv:2403.12147</i>, 2024.","ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains,” <i>arXiv:2403.12147</i>. 2024.","bibtex":"@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains}, journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024} }","ama":"Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains. <i>arXiv:240312147</i>. Published online 2024.","short":"B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024)."},"department":[{"_id":"799"}],"date_created":"2024-03-20T14:56:05Z","external_id":{"arxiv":["2403.12147"]},"_id":"52691","status":"public","year":"2024","author":[{"last_name":"Hinrichs","full_name":"Hinrichs, Benjamin","first_name":"Benjamin","id":"99427","orcid":"0000-0001-9074-1205"},{"full_name":"Matte, Oliver","last_name":"Matte","first_name":"Oliver"}],"user_id":"99427"}