Monte Carlo and quasi-Monte Carlo algorithms for the Barker-Ferry equation with low complexity

Abstract

In this paper we study the possibility to use the Sobol' and Halton quasi-random number sequences (QRNs) in solving the Barker-Ferry (B-F) equation which accounts for the quantum character of the electron-phonon interaction in semiconductors. The quasi-Monte Carlo (QMC) solutions obtained by QRNs are compared with the Monte Carlo (MC) solutions in case when the scalable parallel random number generator (SPRNG) library is used for producing the pseudo-random number sequences (PRNs). In order to solve the B-F equation by a MC method, a transition density with a new sampling approach is suggested in the Markov chain. © Springer-Verlag Berlin Heidelberg 2003.