A time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations
Abstract
In this article, we propose an efficient time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations. The method achieves second-order accuracy in time and spectral accuracy in phase space, both of which are rigorously verified by numerical experiments. The validated scheme is then employed to study the long-time dynamics of these systems. We investigate the existence of steady states for both the Wigner-Fokker-Planck and Wigner-Poisson-Fokker-Planck equations. Notably, for the Wigner-Fokker-Planck system, our results provide numerical evidence for the existence of a steady state even when the external potential is far from harmonic. This is an important discovery, since this phenomenon has not been thoroughly established in theory.
Keywords
Cite
@article{arxiv.2509.11153,
title = {A time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations},
author = {Qian Yi and Limin Xu},
journal= {arXiv preprint arXiv:2509.11153},
year = {2025}
}