Quantum-classical transitions in Lifshitz tails with magnetic fields.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Physics

Background:

• Lifshitz's model describes quantum particles in random potentials.
• The integrated density of states (IDOS) reveals low-energy properties.
• Magnetic fields significantly alter quantum system behaviors.

Purpose of the Study:

• Investigate the impact of a constant magnetic field on the Lifshitz tail of the IDOS.
• Develop a magnetic field analog to Lifshitz's 40-year-old result for short-ranged potentials.
• Analyze the transition of the Lifshitz tail from quantum to classical regimes.

Main Methods:

• Utilized Lifshitz's model for a quantum particle with a repulsive Poissonian random potential.
• Introduced a constant magnetic field into the system.
• Analyzed the behavior of the leading low-energy tail of the IDOS.

Main Results:

• The Lifshitz tail exhibits a transition in character with increasing potential range (U).
• This transition spans from purely quantum to quantum-classical, and finally to purely classical.
• The magnetic field's influence on the IDOS tail was characterized.

Conclusions:

• The observed transition is driven by the interplay between classical potential energy fluctuations and quantum kinetic energy fluctuations.
• The range of the random potential is a critical factor in determining the nature of the Lifshitz tail under a magnetic field.
• This work extends Lifshitz's foundational results to include magnetic field effects in disordered quantum systems.