On the equipartition law in quantum statistical mechanics

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Abstract
The authors prove that the fluctuations of the total momentum of a system of quantum mechanical particles at equilibrium obey the classical equipartition law whenever the correlation functions have an integrable clustering. The result holds for a large class of translation invariant two-body potentials and for arbitrary statistics. They also discuss higher moments of the total momentum and position. Finally the behaviour in models with broken symmetry is analysed.

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