00-330 M.Combescure,D.Robert

Rigorous semiclassical results for the magnetic response of an electron gas (58K, LaTeX) Aug 31, 00

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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}

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