Self-Adjointness and Domain of the Froehlich Hamiltonian
| Autor: | M. Griesemer, A. Wuensch |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Physics
81Q10 81T16 010102 general mathematics Perturbation (astronomy) FOS: Physical sciences Statistical and Nonlinear Physics Electron Mathematical Physics (math-ph) Polaron 01 natural sciences symbols.namesake 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Hamiltonian (quantum mechanics) Mathematical Physics Mathematical physics |
| DOI: | 10.48550/arxiv.1508.02533 |
| Popis: | In the large polaron model of H. Froehlich, the electron-phonon interaction is a small perturbation in form sense, but a large perturbation in operator sense. This means that the form-domain of the Hamiltonian is not affected by the interaction but the domain of self-adjointness is. In the particular case of the Froehlich model, we are nevertheless able, thanks to a recently published new operator bound, to give an explicit characterization of the domain in terms of a suitable dressing transform. Using the mapping properties of this dressing transform, we analyze the smoothness of vectors in the domain of the Hamiltonian with respect to the position of the electron. Comment: 20 pages, with some clarifications and improvements compared to version 1. To appear in Journal of Mathematical Physics |
| Databáze: | OpenAIRE |
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