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Quantum molecular dynamics using Wigner representation

Vladimir S. Filinov, Sara Bonella, Yu. E. Lozovik, Alexey V. Filinov, I. Zacharov

Published Jun 1, 1998• 7 citations
Publisher
DOI
10.1142/9789812839664_0028

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A new numerical approach to time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weil symbol of operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the last function the integral Wigner-Liouville type equation has been derived. The initial condition for this equation has been obtained in the form of the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at initial time. The numerical procedure for solving this equation combining both molecular dynamics and Monte Carlo methods has been developed.
A new method for solving the Wigner-Liouville equation allowing a treatment of quantum dynamics has been developed. The method combines two widely known approaches: molecular dynamics and Monte Carlo. Numerical results have been obtained for one-, two- and three-dimensional potential wells of realistic type. The quantum dynamics method was tested by a comparison of the numerical results with analytical estimates for such values as the average position x¯(t), average momentum p¯(t), energy Ē(t), position and momentum dispersions, and Heisenberg inequality.