Classical stochastic dynamics and extended $N = 4$ supersymmetric quantum mechanics

TL;DR

This paper demonstrates how extended $N=4$ supersymmetric quantum mechanics can be used to construct new exactly-solvable stochastic systems with flexible potentials that do not alter the system's dispersion behavior.

Contribution

It introduces a novel approach using $N=4$ SUSY QM to generate stochastic models with parametric potential freedom, enhancing solvability and control.

Findings

New exactly-solvable stochastic systems constructed

Potentials can be varied without affecting dispersion

Extended supersymmetry provides parametric flexibility

Abstract

This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics ($N=4 SUSY QM$) formalism. A feature of the proposed approach consists in $N=4 SUSY QM$ the fact that probability densities and so obtained new potentials, which enter the Langevin equation, have a parametric freedom. The latter allows one to change the potentials form without changing the temporal behavior of the dispersion function.