Ground State Properties in the Quasi-Classical Regime
| Autor: | Correggi, Michele, Falconi, Marco, Olivieri, Marco |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Analysis & PDE 16 (2023) 1745-1798 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/apde.2023.16.1745 |
| Popis: | We study the ground state energy and ground states of systems coupling non-relativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasi-classical approximation. The latter is very useful whenever the force-carrying field has a very large number of excitations,and thus behaves in a semiclassical way, while the non-relativistic particles, on the other hand, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to the one of a nonlinear quasi-classical functional depending on both the particles' wave function and the classical configuration of the field. Equivalently, this energy can be interpreted as the lowest energy of a Pekar-like functional with an effective nonlinear interaction for the particles only. If the particles are confined, the ground state of the microscopic system converges as well, to a probability measure concentrated on the set of minimizers of the quasi-classical energy. Comment: 52 pages, pdfLaTeX |
| Databáze: | arXiv |
| Externí odkaz: |
|