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Value statistics of chaotic Wigner function

Martin Horvat·Tomaz Prosen
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Abstract

We study Wigner function value statistics of classically chaotic quantum maps on compact 2D phase space. We show that the Wigner function statistics of a random state is a Gaussian, with the mean value becoming negligible compared to the width in the semi-classical limit. Using numerical example of quantized sawtooth map we demonstrate that the relaxation of time-dependent Wigner function statistics, starting from a coherent initial state, takes place on a logarithmically short log (hbar) time scale.

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Martin Horvat, Tomaz Prosen. 2006-02-01. Value statistics of chaotic Wigner function. https://arxiv.org/abs/quant-ph/0602007

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