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.

Ground State Properties in the Quasi-Classical Regime

M. Correggi;M. Falconi;
2023-01-01

Abstract

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.
2023
Quasi-classical limit, Interaction of matter and light, Semiclassical analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1219253
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