About Speakers Schedule School of Mathematical Sciences, SJTU INS, SJTU
动理学与流体力学方程研讨会

Numerical simulations of 6-D and 12-D quantum kinetic equations

Speaker

熊云丰 , 北京师范大学

Time

08 Apr, 14:00 - 14:45

Abstract

The phase-space formulation of quantum mechanics, say, the Wigner equation, has recently been drawing a growing interest in semiconductor device simulations, nuclear fusion and quantum tomography. However, numerical resolution for realistic 6-D problem (3-D position plus 3-D momentum) faces with combined challenges of high dimensionality, nonlocality, oscillation and singularity. In particular, the extremely huge memory storage of 6-D grids hinders the usage of all existing deterministic numerical scheme, which is well-known as the curse of dimensionality. In this talk, I would like to report our recent progress in simulating 6-D Wigner equation under the Coulomb potential. First, I would like to report our massively parallel deterministic algorithm and present the interacting picture of a quantum electron interacting with a proton. After that, we will discuss a recently developed stochastic Wigner algorithm by exploiting the branching random walk interpretation to the Wigner equation, which may potentially be applicable for solving 12-D problem and further overcome the curse of dimensionality.