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Published March 14, 2020 | Submitted + Published
Journal Article Open

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.

Additional Information

© 2020 Published under license by AIP Publishing. Submitted: 19 December 2019; Accepted: 24 February 2020; Published Online: 12 March 2020. The authors would like to thank Rob Jack, Vivien Lecomte, Juan P. Garrahan, and David Limmer for fruitful and engaging discussions. U.R. was supported by the Simons Collaboration on the Many-Electron Problem and the California Institute of Technology. G.K.-L.C. is a Simons Investigator in Theoretical Physics and was supported by the California Institute of Technology and the U.S. Department of Energy, Office of Science, via Grant No. DE-SC0018140. These calculations were performed with CANSS, available at https://github.com/ushnishray/CANSS.

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Published - 1.5143144.pdf

Submitted - 1909.11283v3.pdf

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Additional details

Created:
August 19, 2023
Modified:
October 19, 2023