Metastable states, transitions, basins and borders at finite temperatures

TL;DR

This paper explores the use of supersymmetry in Langevin/Fokker-Planck processes to analyze metastable states, barriers, and reaction paths at finite temperatures, providing new insights and computational methods for complex systems.

Contribution

It introduces a supersymmetric framework to study non-zero fermion subspaces in Langevin/Fokker-Planck processes, enhancing analysis of barriers and unstable states at finite temperatures.

Findings

New computational strategies for barriers and reaction paths.

Analysis of metastable states in non-zero temperature systems.

Application to systems with entropic or collective barriers.

Abstract

Langevin/Fokker-Planck processes can be immersed in a larger frame by adding fictitious fermion variables. The (super)symmetry of this larger structure has been used to derive Morse theory in an elegant way. The original physical diffusive motion is retained in the zero-fermion subspace. Here we study the subspaces with non-zero fermion number which yield deep information, as well as new computational strategies, for barriers, reaction paths, and unstable states -- even in non-zero temperature situations and when the barriers are of entropic or collective nature, as in the thermodynamic limit. The presentation is self-contained.