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Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states

Helms, Phillip and Ray, Ushnish and Chan, Garnet Kin-Lic (2019) Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states. Physical Review E, 100 (2). Art. No. 022101. ISSN 2470-0045. http://resolver.caltech.edu/CaltechAUTHORS:20190528-085213219

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Abstract

The open asymmetric simple exclusion process (ASEP) has emerged as a paradigmatic model of nonequilibrium behavior, in part due to its complex dynamical behavior and wide physical applicability as a model of driven diffusion. We compare the dynamical phase behavior of the one-dimensional (1D) ASEP and the multi-lane ASEP, a previously unstudied extension of the 1D model that may be thought of as a finite-width strip of the fully two-dimensional (2D) system. Our characterization employs large deviation theory (LDT), matrix product states (MPS), and the density matrix renormalization group (DMRG) algorithm, to compute the current cumulant generating function and its derivatives, which serve as dynamical order parameters. We use this measure to show that when particles cannot exit or enter the lattice vertically, the phase behavior of the multi-lane ASEP mimics that of its 1D counterpart, exhibiting the macroscopic and microscopic signatures of the maximal current, shock, and high-density–low-density coexistence phases. Conversely, when particles are allowed to freely enter and exit the lattice, no such transition is observed. This contrast emphasizes the complex interplay between latitudinal and longitudinal hopping rates and the effect of current biasing. Our results support the potential of tensor networks as a framework to understand classical nonequilibrium statistical mechanics.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevE.100.022101DOIArticle
https://arxiv.org/abs/1904.07336arXivDiscussion Paper
ORCID:
AuthorORCID
Helms, Phillip0000-0002-6064-3193
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2019 American Physical Society. Received 17 April 2019; published 2 August 2019. This work was supported primarily by the US National Science Foundation (NSF) via Grant No. CHE-1665333. P.H. was also supported by a NSF Graduate Research Fellowship under Grant No. DGE-1745301 and an ARCS Foundation Award.
Funders:
Funding AgencyGrant Number
NSFCHE-1665333
NSF Graduate Research FellowshipDGE-1745301
ARCS FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20190528-085213219
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190528-085213219
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95806
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 May 2019 16:13
Last Modified:05 Aug 2019 16:26

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