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

Fuente: arXiv
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Autor principal: Ho, Choon-Lin
Formato: Preprint
Publicado: 2021
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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