Persistence of the spectral gap for the Landau-Pekar equations

TL;DR

This paper demonstrates that for certain initial conditions, the spectral gap of the effective Hamiltonian in the Landau-Pekar equations remains uniform over time, enabling extended adiabatic analysis.

Contribution

It establishes the persistence of the spectral gap for specific initial data, extending the adiabatic theorem to larger times in the Landau-Pekar model.

Findings

Spectral gap remains uniform over time for chosen initial data

Extended validity of the adiabatic theorem for the Landau-Pekar equations

Improved understanding of the dynamics of strongly coupled polarons

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.