Department of Mathematical Sciences
题目: Analysis of the moment closure for Spin-Boson model in quantum open system
摘要：Motivated by the numerical study of the spin-boson dynamics in quantum open systems, we present a convergence analysis of the moment closure approximation for a class of stochastic differential equations. We show that the naive Monte Carlo simulation of the system by direct tem- poral discretization is not feasible through variance analysis and numerical experiments. We also show that the Wiener chaos expansion exhibits very slow convergence and high computational cost. Though efficient and accurate, the rationale of the moment closure approach remains mysterious. We rigorously prove that the low moments in the moment closure approximation of the considered model are of exponential convergence to the exact result. It is further extended to more general nonlinear problems with similar structure. The application to the original spin-boson model is also discussed.