I am working on the numerical methods for kinetic theory. Specifically, we are exploring low-rank properties of the solution and try to apply some low-rank methods to solve the kinetic equations.
I am working on the numerical methods for open quantum systems. We designed the differential equation based path integral (DEBPI), the bold-thin-bold Monte Carlo (BTB) method, tree-based implementation for small matrix path integral (t-SMatPI) for the simulation of spin-boson model. We derived a brand new method for the simulation of dissipative spin chain based on modular path integral (MPI) and inchworm algorithm. We also work on the numerical simulation of the Caldeira-Leggett model and fast resummation of Dyson series. Tensor tools are applied in these methods.
(The following collaborators are ranked alphabetically by surnames. Click their names for their homepages)
Dr. Zhenning CAI, National University of Singapore
Dr. Jingwei HU, University of Washington
Ms. Yixiao SUN, National University of Singapore
Dr. Siyao YANG, University of Chicago