Large deviations for ideal quantum systems

Details Large deviations for ideal quantum systems Large deviations for ideal quantum systems

1999-06-16

arxiv.org/abs/math-ph/9906014v1

J. Math. Phys. 41 (2000), no. 3, 1224-1243

Physics

Mathematical Physics

28 pages, LaTeX 2e

Scientific paper

10.1063/1.533185

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.

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