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arXiv · 2109.03854

Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations

Choon-Lin Ho
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Abstract

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 Schr\"odinger equation. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schr\"odinger 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.

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BibTeXRIS

Choon-Lin Ho. 2021-09-08. Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations. https://doi.org/10.1016/j.cjph.2021.12.028

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