Stochastic wave-function method versus density matrix: a numerical comparison Original Research Article

Numerical investigations of open quantum systems, which are widely performed in such fields as photochemistry, quantum optics and nuclear magnetic resonance, can, in the Markovian regime, be based either on the master equation for the reduced density operator or on a stochastic process in the Hilbert space of the reduced system. It is shown that the CPU time consumptions of the two methods depend on the system size N as Nα+1 and as R(N)Nα, respectively. The exponent α is characteristic of the specific system. R(N) is the number of process realizations generated in the simulation and is defined by prescribing the tolerable statistical error of the result. Since R(N) is a non-increasing function of N, the stochastic method is found to be always faster for large systems. This is demonstrated for the example of the dissipative Morse oscillator excited by an intense short laser pulse.