Persistence of the spectral gap for the Landau-Pekar equations

Abstract

The Landau-Pekar equations describe the dynamics of a strongly coupled polaron. Here we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau-Pekar equations and their derivation from the Froehlich model obtained in [8, 7] to larger times.

arXiv comment15 pages

References in corpus (2)

• Uniqueness of Ground States for Pseudo-Relativistic Hartree Equations
• Derivation of an effective evolution equation for a strongly coupled polaron

Cited by in corpus (8)

• The Landau-Pekar equations: Adiabatic theorem and accuracy
• 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
• The effective mass problem for the Landau-Pekar equations
• Ubiquity of bound states for the strongly coupled polaron
• The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling