Rigorous semiclassical results for the magnetic response of an electron gas

Details Rigorous semiclassical results for the magnetic response of an electron gas Rigorous semiclassical results for the magnetic response of an electron gas

2000-08-31

arxiv.org/abs/math-ph/0008041v1

Physics

Mathematical Physics

Scientific paper

10.1142/S0129055X01000971

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 $\hbar$ (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 $\hbar$-expansions. In particular when $T$ is of the order of $\hbar$, oscillations ``\`a la de Haas-van Alphen'' appear, that can be linked to the classical periodic orbits of the electronic motion.

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