Unitary integration with operator splitting for weakly dissipative systems

Unitary integration is a numerical method that preserves the structure of the quantum Liouville equation by evolving the density via unitary transformations. Unitary integrators preserve the kinematic invariants cj=trρj (j=1,...,n) to all orders in the time step. Here we extend unitary integration to weakly dissipative systems. We apply the technique of operator splitting, using a unitary integrator for the Hamiltonian evolution and a conventional integrator for the dissipative piece. In this way, we guarantee that all dissipation and decoherence (variation of the cj) is due to the new non-Hamiltonian terms and not to any numerical artifacts. We illustrate the method with examples. (author)