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

Abstract

This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics ($N=4SUSYQM$) formalism. A feature of the proposed approach consists in $N=4SUSYQM$ 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.

Proceedings of NPQCD 2009, Dnipropetrovsk, Ukraine