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arXiv:2307.16613 · Journal of Statistical Physics

Semiclassical Approximation of the Wigner Function for the Canonical Ensemble

M. Gil de Oliveira, Alfredo M. Ozorio de Almeida

Published Sep 24, 2023• 1 citation
arXivHTMLPDF
DOI
10.1007/s10955-023-03164-w

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The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of the strongly interacting systems of particles has been developed for extreme conditions, when there are no small physical parameters and analytical approximations used in different kind of perturbation theories can not be applied. The new path integral representation of the quantum Wigner function in the phase space has been developed for canonical ensemble. Explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. The new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been proposed. Preliminary calculations of the momentum distribution function of the Coulomb systems of particles have been carried out. Comparison with classical Maxwell-Boltzmann distribution shows the significant influence of quantum effects on the high energy asymptotics ("tails') of the calculated momentum distribution functions, which resulted in appearance of sharp oscillations.