M.Combescure,D.Robert
Rigorous semiclassical results for the magnetic response of an electron gas
(58K, LaTeX)
ABSTRACT. \begin{document}
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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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