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Large deviations for ideal quantum systems

Joel L. Lebowitz·Marco Lenci·Herbert Spohn
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Abstract

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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Joel L. Lebowitz, Marco Lenci, Herbert Spohn. 1999-06-16. Large deviations for ideal quantum systems. https://doi.org/10.1063/1.533185

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