Supersymmetries in nonequilibrium Langevin dynamics

Area of Science:

• Statistical Mechanics
• Theoretical Physics
• Nonlinear Dynamics

Background:

• Langevin equations model stochastic phenomena and microscopic dynamics.
• Reversible dynamics exhibit supersymmetries (SUSYs) related to path-integral formulations.
• Existing SUSY constructions are limited to equilibrium systems.

Purpose of the Study:

• To extend the concept of supersymmetry to irreversible dynamics in overdamped Langevin equations.
• To investigate the relationship between these generalized SUSYs, time-reversal symmetry, and nonequilibrium fluctuation-dissipation relations.
• To provide a concrete example using the Kardar-Parisi-Zhang equation.

Main Methods:

• Developing a generalized Parisi-Sourlas supersymmetry construction for irreversible Langevin dynamics.
• Utilizing the non-uniqueness of Grassmannian representations for functional determinants.
• Analyzing the connection between generalized SUSYs and modified fluctuation-dissipation theorems.

Main Results:

• Demonstrated that supersymmetries can be extended to arbitrary irreversible overdamped Langevin equations with additive white noise, given knowledge of their steady state.
• Established a link between these generalized SUSYs and time-reversal symmetries.
• Derived modified fluctuation-dissipation relations applicable to nonequilibrium systems.
• Applied the framework to the Kardar-Parisi-Zhang equation.

Conclusions:

• The study successfully extends supersymmetry to irreversible stochastic dynamics, challenging previous assumptions.
• The derived modified fluctuation-dissipation relations offer new tools for analyzing systems out of equilibrium.
• The findings have implications for understanding complex systems in physics and beyond.