A short-time quantum mechanical expansion approach to vibrational relaxation

The vibrational relaxation rate of a "quantum" molecule embedded in a "quan tum" host is approached from the perspective of a short-time expansion of t he quantum force-force time correlation function. A general path integral M onte Carlo scheme is developed to compute the coefficients of the expansion , which involve the quantum thermal average of operators that depend on bot h position and momentum. A simple ansatz is used to connect the short-time and long-time behavior of the force-force correlation function. The method is tested on a simple model problem. Improvements of the approach and furth er applications are discussed.