# Ground State Properties in the Quasi-Classical Regime

## Metadata

### APDE 16(8), 1745-1798

The published version is available open access (subscribe to open) at msp.

### arXiv 2007.09442

The preprint in pdf is available at arXiv.org.

### Bibtex

The bibtex entry for the article can be downloaded here.

## 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 particlesâ€™ 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.