Generalized susceptibilities for a perfect quantum gas

Details Generalized susceptibilities for a perfect quantum gas Generalized susceptibilities for a perfect quantum gas

2006-05-05

arxiv.org/abs/math-ph/0605019v1

Markov Process. Related Fields vol. 11 no. 2, 177--188 (2005)

Physics

Mathematical Physics

Appeared in MPRF

Scientific paper

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 $\Lambda$ with side $L\geq 1$, and subjected to a constant magnetic field of intensity $ B \geq 0 $. Define the grand canonical generalized susceptibilities $\chi_L^N$, $N\geq 1$, 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 $\chi_L^N$ 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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