Rigorous semiclassical results for the magnetic response of an electron gas

Abstract

Consider a free electron gas in a confining potential and a magnetic field in arbitrary dimensions. If this gas is in thermal equilibrium with a reservoir at temperature $T>0$, one can study its orbital magnetic response (omitting the spin). One defines a conveniently ``smeared out'' magnetization $M$, and the corresponding magnetic susceptibility $\chi$, which will be analyzed from a semiclassical point of view, namely when $\hslash$ (the Planck constant) is small compared to classical actions characterizing the system. Then various regimes of temperature $T$ are studied where $M$ and $\chi$ can be obtained in the form of suitable asymptotic $\hslash$-expansions. In particular when $T$ is of the order of $\hslash$, oscillations ``à la de Haas-van Alphen'' appear, that can be linked to the classical periodic orbits of the electronic motion.

References in corpus (1)

• A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition

Cited by in corpus (5)

• Coherent-State Approach to Two-dimensional Electron Magnetism
• A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit
• Diamagnetism of quantum gases with singular potentials
• Semiclassical results in the linear response theory
• Magnetism of Two Coupled Harmonic Oscillators