Selected topics in transport phenomena: deterministic and probabilistic aspects

Stochastic algorithms for high dimensional transport systems

Jianfeng Lu

Duke University

In this talk, we will discuss our recent work on a surface hopping Gaussian beam method for high dimensional transport systems, in particular, the quantum-classical Liouville equations arising from semiclassical Schrödinger dynamics in the non-adiabatic regime. If time permits, we will also discuss a quantum kinetic Monte Carlo algorithm for spin dynamics. These methods are based on a common design principle of stochastic approximation of a series expansion from time dependent perturbation theory. Joint work with Zhenning Cai (NUS).