QUANTUM DYNAMICS IN CANONICAL AND MICRO-CANONICAL ENSEMBLES - PART II- TUNNELING IN DOUBLE-WELL POTENTIAL

In the second part of this paper on micro-canonical ensemble a new num erical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation funct ions 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 Weyl's symbol of the considered opera tors and the Fourier transform of the product of matrix elements of th e dynamic propagators. For the latter function the integral Wigner-Lio uville's type equation has been derived. The initial condition for thi s equation has been obtained in the form of the Fourier transform of t he Wiener path integral representation of the matrix elements of the p ropagators at initial time. A numerical procedure for solving this equ ation combining both molecular dynamics and Monte Carlo methods has be en developed. Numerical results have been obtained for series of avera ge values of the quantum operators as well as for the time correlation function characterizing the energy level structure, the momentum flow of tunnelling particles at barrier crossing and the absorption spectr a of electrons in a potential well. The developed quantum dynamics met hod was tested by comparison of numerical results with analytical esti mations. Tunnelling transitions and the effect of the quasi stationary state have been considered as the reasons for the peculiarities in be haviour of the time correlation functions and position and momentum di spersions. The possibility of applying the developed approach to the t heory of classical wave propagation in random media have also been con sidered. For classical waves some results have been obtained for Gauss ian beam propagation in 2D and 3D waveguides.