Quantum and classical stochastic dynamics: Exactly solvable models by supersymmetric methods

TL;DR

This paper reviews and extends supersymmetric methods to construct exactly solvable models in both quantum and classical stochastic dynamics, providing explicit solutions and decay rates for various drift potentials.

Contribution

It introduces a supersymmetric approach to solve classical stochastic systems with Fokker-Planck equations, expanding the class of exactly solvable models.

Findings

Explicit solutions for drift potentials on the real line and half line.

Closed-form decay rates and modes for mono-, bi-, meta-stable systems.

Extension of supersymmetric methods to classical stochastic dynamics.

Abstract

A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of drift-potentials on the real line as well as on the half line is constructed for which the associated Fokker-Planck equation can be solved exactly. Explicit drift potentials, which describe mono-, bi-, meta-or unstable systems, are constructed and their decay rates and modes are given in closed form.