Numerical implementation of a mixed quantum classical rate theory

The recently formulated mixed quantum classical rate theory (MQCLT) is impl emented for a model system with two degrees of freedom. In MQCLT, one must compute the Wigner representation of the symmetrized thermal flux operator. This phase space flux distribution is then multiplied by the classical rea ction probability to obtain the rate. The major computational difficulty is the multidimensional Fourier transform necessary for obtaining the Wigner distribution. The Fourier transform reintroduces a sign problem when attemp ting to estimate the MQCLT rate using Monte Carlo methods. Two different me thods for overcoming the sign problem are explored in this paper. Numerical results are presented for a model problem of an Eckart barrier coupled bil inearly to a slow oscillator and compared with numerically exact results. ( C) 1999 American Institute of Physics. [S0021-9606(99)02740-3].