A time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914036282556416 |
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| author | Yi, Qian Xu, Limin |
| author_facet | Yi, Qian Xu, Limin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations Yi, Qian Xu, Limin Numerical Analysis Computational Physics 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. |
| title | A time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2509.11153 |