Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909135755280384 |
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| author | Ho, Choon-Lin |
| author_facet | Ho, Choon-Lin |
| contents | A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schrödinger equation. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schrödinger equation. From a solution of a Fokker-Planck equation a solution of the Darboux partner is obtained. For drift coefficients satisfying the condition of shape invariance, a supersymmetric hierarchy of Fokker-Planck equations with solutions related by the Darboux transformation is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_03854 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations Ho, Choon-Lin Mathematical Physics Statistical Mechanics Exactly Solvable and Integrable Systems Quantum Physics A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schrödinger equation. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schrödinger equation. From a solution of a Fokker-Planck equation a solution of the Darboux partner is obtained. For drift coefficients satisfying the condition of shape invariance, a supersymmetric hierarchy of Fokker-Planck equations with solutions related by the Darboux transformation is obtained. |
| title | Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations |
| topic | Mathematical Physics Statistical Mechanics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2109.03854 |