Ground State Properties in the Quasi-Classical Regime

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.

52 pages, pdfLaTeX

References in corpus (5)

• Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
• Self-Adjointness criterion for operators in Fock spaces
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• A note on the Fröhlich dynamics in the strong coupling limit
• A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations

Cited by in corpus (4)

• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Quasi-classical Limit of a Spin Coupled to a Reservoir
• Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields
• Convergence of states for polaron models in the classical limit