Quantum corrections to the Pekar asymptotics of a strongly coupled polaron

Abstract

We consider the Fröhlich polaron model in the strong coupling limit. It is well known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem.

LaTeX, 40 pages; final version, to appear in Commun. Pure. Appl. Math

References in corpus (3)

• Identification of the Polaron measure in strong coupling and the Pekar variational formula
• Uniqueness and Non-Degeneracy of Minimizers of the Pekar Functional on a Ball
• Strong coupling limit of the Polaron measure and the Pekar process

Cited by in corpus (13)

• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• Quasi-Classical Dynamics
• A note on the Fröhlich dynamics in the strong coupling limit
• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Polaron models with regular interactions at strong coupling
• The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics
• The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
• Ground State of the Polaron Hydrogenic Atom in a Strong Magnetic Field
• Convergence of states for polaron models in the classical limit
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling
• Bound excited states of Fröhlich polarons in one dimension