Quantum-classical transitions in Lifshits tails with magnetic fields

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.

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Cited by in corpus (3)

• Functionals of the Brownian motion, localization and metric graphs
• The Integrated Density of States for Random Schroedinger Operators
• Tails of the Density of States in a Random Magnetic Field