2025/09/14 by Qian Yi, Yi, Qian, Limin Xu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2509.11153
openalex publication_date 2025/09/14 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
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.