Two-dimensional Fokker-Planck solutions and Grassmann variables

TL;DR

This paper explores solutions to the two-dimensional Fokker-Planck equation using Grassmann variables, revealing how spatial inhomogeneities relate to underlying Grassmannian pseudo-degrees of freedom, with potential extensions to higher dimensions.

Contribution

It introduces a novel interpretation of 2D Fokker-Planck solutions through Grassmann variables, linking spatial inhomogeneities to pseudo-degrees of freedom.

Findings

Spatial inhomogeneities linked to Grassmannian pseudo-degrees of freedom.

Extension of Grassmannian interpretation to higher-dimensional FP solutions.

Provides a factorization framework for 2D FP equations using Grassmann variables.

Abstract

After a short outline of the factorization and Grassmann picture of the one-dimensional (1D) Fokker-Planck (FP) equation, we consider a class of spatially-inhomogeneous solutions of the 2D FP equation with symmetric 2D (super)potentials. We show that the spatial inhomogeneities of that class of solutions can be attributed to underlying Grassmannian pseudo-degrees of freedom. Such an interpretation may also be applied to FP solutions in three and more dimensions.