Quantum-classical transitions in Lifshits tails with magnetic fields

TL;DR

This paper investigates how a magnetic field affects the low-energy tail of the density of states in a quantum particle system with random potential, revealing a transition from quantum to classical behavior as potential range increases.

Contribution

It introduces the magnetic analog of Lifshits' classical result, analyzing the transition of the Lifshits tail from quantum to classical regimes with varying potential range.

Findings

Lifshits tail changes from quantum to classical with increasing potential range

Magnetic field influences the nature of the low-energy tail

Classical fluctuations dominate over quantum fluctuations at large potential ranges

Abstract

We consider Lifshits' model of a quantum particle subject to a repulsive Poissonian random potential and address various issues related to the influence of a constant magnetic field on the leading low-energy tail of the integrated density of states. In particular, we propose the magnetic analog of a $ 40 $-year-old landmark result of Lifshits for short-ranged single-impurity potentials $ U $. The Lifshits tail is shown to change its character from purely quantum, through quantum-classical, to purely classical with increasing range of $ U $. This systematics is explained by the increasing importance of the classical fluctuations of the particle's potential energy in comparison to the quantum fluctuations associated with its kinetic energy.