Polaron models with regular interactions at strong coupling

Abstract

We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau--Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.

arXiv commentLaTeX, 22 Pages. Minor changes, published version

References in corpus (15)

• Erratum: Exact Ground State Energy of the Strong-Coupling Polaron
• Strong coupling Bose polarons in a two-dimensional gas
• Strong coupling treatment of the polaronic system consisting of an impurity in a condensate
• Feynman path-integral treatment of the Bose polaron beyond the Fröhlich model
• New theoretical approaches to Bose polarons
• Quantum corrections to the Pekar asymptotics of a strongly coupled polaron
• Mean-field study of repulsive 2D and 3D Bose polarons
• Divergence of the effective mass of a polaron in the strong coupling limit
• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• Effective mass of the polaron -- revisited
• Quantum groups as hidden symmetries of quantum impurities
• Equivalence of two definitions of the effective mass of a polaron
• A note on the Fröhlich dynamics in the strong coupling limit
• A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics
• The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics

Cited by in corpus (1)

• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron