DISCRETE TIME-REVERSIBLE PROPAGATION SCHEME FOR MIXED QUANTUM-CLASSICAL DYNAMICS

A time-reversible multiple time step quantum-classical propagation sch eme within the time-dependent self-consistent field approximation (TDS CF) is presented. The equations of motion are obtained by transforming the time-dependent Schrodinger equation into a Hamilton-Jacobi-type f ormalism and describing the mixed quantum-classical time evolution by means of a Liouville operator, derived from a classical-type Hamiltoni an, acting on a generalized phase space. The method is applied to a mo del system consisting of a harmonic oscillator non-linearly coupled to a bath of argon atoms and numerically tested with respect to norm and energy conservation and time-reversibility. The time-reversible multi ple time step propagation scheme significantly contributes to the nume rical stability in comparison to a non-reversible propagator with the same computational effort.