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Generalized susceptibilities for a perfect quantum gas

Philippe Briet·Horia D. Cornean·Delphine Louis
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Abstract

The system we consider here is a charged fermions gas in the effective mass approximation, and in grand-canonical conditions. We assume that the particles are confined in a three dimensional cubic box $Λ$ with side $L\geq 1$, and subjected to a constant magnetic field of intensity $ B \geq 0 $. Define the grand canonical generalized susceptibilities $χ_L^N$, $N\geq 1$, as successive partial derivatives with respect to $B$ of the grand canonical pressure $P_L$. Denote by $P_{\infty}$ the thermodynamic limit of $P_L$. Our main result is that $χ_L^N$ admit as thermodynamic limit the corresponding partial derivatives with respect to $B$ of $P_{\infty}$. In this paper we only give the main steps of the proofs, technical details will be given elsewhere.

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Philippe Briet, Horia D. Cornean, Delphine Louis. 2006-05-05. Generalized susceptibilities for a perfect quantum gas. https://arxiv.org/abs/math-ph/0605019

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