M.Combescure,D.Robert
Rigorous semiclassical results for the magnetic response of an electron gas
(58K, LaTeX)

ABSTRACT.  \begin{document} 
\baselineskip = 24 pt 
\centerline{\bf Abstract :} 
\vskip 3 truemm 
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. 
\end{document}