Sequential short-time propagation of quantum-classical dynamics

An algorithm for the simulation of quantum-classical dynamics is presented. Quantum-classical evolution is effected by a propagator exp(i (L) over capt) involving the quantum classical Liouville operator (L) over cap that describes the evolution of a quantum subsystem coupled to a classical bath. Such a mixed description provides a means to study the dynamics of complex many-body systems where certain degrees of freedom are treated quantum mechanically. The algorithm is constructed by decomposing the time interval Deltat into small segments of length At and successively applying the propagator in the short time segments to obtain the evolution for long times. The algorithm is shown to be a discretization of the iterated Dyson form of the propagator whose direct solution is vexatious. The sequential short-time propagation algorithm is applied to the spin-boson model for a range of values of the Kondo parameter and shown to be effective.