My research interests include:

• Modeling and numerical simulation for rarefied gases
• Numerical methods for open quantum systems
• Complex Langevin method in quantum chromodynamics

Modeling and numerical simulation for rarefied gases

I am developing a deterministic numerical solver for the Boltzmann equation with quadratic collision terms. The method is based on the Burnett spectral method and the discontinuous Galerkin method. I am also working on modeling rarefied gases using moment methods. I established a framework to develop hyperbolic moment equations, which can be applied to a wide range of kinetic equations. I am also working on regularized 13-moment equations for moderately rarefied gases with general potentials between gas molecules.

Numerical methods for open quantum systems

I am working on the numerical schemes and numerical analysis for open quantum systems, which couple a quantum system we are interested in and the environment. The surface hopping method and the inchworm Monte Carlo method are being developed and analyzed, and I’m also studying the iterative QuAPI method and trying to improve the performance.

Complex Langevin method in quantum chromodynamics

I am studying the mechanism of complex Langevin method as a stochastic method to calculate integrals. By investigating some special cases, we are trying to describe the typical behavior of the method, especially when the method generates incorrect results. I am also working on better algorithms to apply the gauge cooling technique, which can significantly stabilize the method.

Research Group Members

• Ernest PAN, PhD student, August 2024 to present
• Yixiao SUN, PhD student, August 2023 to present
• Geshuo WANG, Research fellow, January 2024 to present
• Haoxuan WANG, PhD Student, August 2018 to present