Discrete time-reversible propagation scheme for mixed quantum-classical dynamics Original Research Article

A time-reversible multiple time step quantum-classical propagation scheme within the time-dependent self-consistent field approximation (TDSCF) is presented. The equations of motion are obtained by transforming the time-dependent Schrödinger equation into a Hamilton-Jacobi-type formalism and describing the mixed quantum-classical time evolution by means of a Liouville operator, derived from a classical-type Hamiltonian, acting on a generalized phase space. The method is applied to a model 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 multiple time step propagation scheme significantly contributes to the numerical stability in comparison to a non-reversible propagator with the same computational effort.