Supersymmetric properties of one-dimensional reversible Markov generators with the links to Markov-dualities and to shape-invariance-exact-solvability
Abstract
Abstract For one-dimensional reversible diffusion process involving the force F ( x ) and the diffusion coefficient D ( x ), the continuity equation ∂ t P t ( x ) = − ∂ ∂ x J t ( x ) gives the dynamics of the probability P t ( x ) in terms of the divergence of the current J t ( x ) = F ( x ) P t ( x ) − D ( x ) ∂ ∂ x P t ( x ) = J P t ( x ) obtained from P t ( x ) via the application of the first-order differential current-operator J . So the dynamics of the probability P t ( x ) is governed by the factorized Fokker–Planck generator F = − ∂ ∂ x J , while the dynamics of the current J t ( x ) is governed by its supersymmetric partner
Fields of Study & Subjects
Topological and Geometric Data Analysis
advanced mathematical theories
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Publisher
- IOP Publishing
- Volume
- 59
- Issue
- 10
- Pages
- 105001–105001
- Publication date
- 27 February 2026
- Language
- EN