Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Complex Systems

Background:

• Monte Carlo methods often suffer from exponentially growing variance in estimating large deviation functions.
• Understanding nonequilibrium systems requires robust computational tools to handle complex dynamics and correlations.

Purpose of the Study:

• To develop a novel strategy for constructing guiding distribution functions (GDFs) to mitigate variance in Monte Carlo estimators.
• To apply this variance minimization technique to analyze interacting driven diffusive systems and lattice models.

Main Methods:

• Constructing guiding distribution functions (GDFs) based on variance minimization.
• Exploiting properties of eigenstates of the tilted operator for biased dynamics.
• Applying correlator product state ansatz for lattice-based simulations.

Main Results:

• Demonstrated variance mitigation in continuum models, improving efficiency by incorporating higher correlations into GDFs.
• Successfully captured phase transition features in the 1D weakly asymmetric simple exclusion process using lattice simulations.
• Showcased the ability to study susceptibility and transport properties in large systems.

Conclusions:

• The variance minimization strategy provides an effective tool for studying large deviation functions in nonequilibrium systems.
• This approach enhances the efficiency and accuracy of simulations for complex physical phenomena.
• The developed methods offer new capabilities for investigating nonequilibrium properties in realistic systems.