Efficiency of different numerical methods for solving Redfield equations

The numerical efficiency of different schemes for solving the Liouvillevon Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different implementations as well as methods especially developed for time propagation: the Short Iterative Arnoldi, Chebyshev and Newtonian propagators. In addition, an implementation of a symplectic integrator has been studied. For a simple example of a two-center electron transfer system we discuss some aspects of the efficiency of these methods to integrate the equations of motion. Overall for time-independent potentials the Newtonian method is recommended. For time-dependent potentials implementations of the RungeKutta algorithm are very efficient. PACS: 02.60.Cb, 31.70.Hq, 34.70.+e