Ground state properties in the quasiclassical regime

We study the ground state energy and ground states of systems coupling nonrelativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasiclassical 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 nonrelativistic particles, on the other hand, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to that of a nonlinear quasiclassical 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 quasiclassical energy.