Title: Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization

Abstract

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study the interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D weakly asymmetric simple exclusion process. We show that with modest resources, we can capture the features of the susceptibility in large systems that mark the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.

Authors:

Ray, Ushnish  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-1850-4691"

Kin-Lic Chan, Garnet ^[1]

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1. California Institute of Technology (CalTech), Pasadena, CA (United States)

Publication Date:

Thu Mar 12 00:00:00 EDT 2020

Research Org.:

California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1803263

Alternate Identifier(s):

OSTI ID: 1604237

Grant/Contract Number:  

SC0018140

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Chemical Physics

Additional Journal Information:

Journal Volume: 152; Journal Issue: 10; Journal ID: ISSN 0021-9606

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemistry; Physics