Localization in the Disordered Holstein model

TL;DR

This paper proves localization phenomena in a disordered Holstein model with small hopping, showing that the particle's position remains localized despite potential tunneling in the quantum field configurations.

Contribution

It provides a rigorous proof of localization in the disordered Holstein model with small hopping amplitude, extending understanding of quantum particle-field interactions.

Findings

Localization of resolvent matrix elements in particle position and Fock space

Dynamical localization of the particle position

Open possibility of resonant tunneling in Fock space

Abstract

The Holstein model describes the motion of a tight-binding tracer particle interacting with a field of quantum harmonic oscillators. We consider this model with an on-site random potential. Provided the hopping amplitude for the particle is small, we prove localization for matrix elements of the resolvent, in particle position and in the field Fock space. These bounds imply a form of dynamical localization for the particle position that leaves open the possibility of resonant tunneling in Fock space between equivalent field configurations.