An efficient backward Monte Carlo estimator for solving of a quantum-kinetic equation with memory kernel

An efficient backward Monte Carlo (MC) estimator and a corresponding algorithm for solving a quantum-kinetic equation describing an ultrafast semiconductor carrier transport is proposed and studied. In order to obtain the electron energy distribution for long evolution times, variance reduction techniques are applied. The balancing of errors (both systematic and stochastic) and computational cost are investigated. The presented algorithm is implemented using the scalable parallel random number generator (SPRNG) and one by P. L'Ecuyer based on a combination of two linear congruential sequences. Numerical results for long and short evolution times are obtained. They show that the SPRNG is preferable to that by P. L'Ecuyer. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.