Numerical method for accessing the universal scaling function for a multiparticle discrete time asymmetric exclusion process

Nicholas D Chia, Ralf Bundschuh

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz's original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N→) of a single-particle discrete time system, even in the case of very small system sizes (N≤22). This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP.

Original languageEnglish (US)
Article number051102
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume72
Issue number5
DOIs
StatePublished - Nov 2005
Externally publishedYes

Fingerprint

Asymmetric Exclusion Process
Universal Function
Scaling Function
exclusion
Universality
Discrete-time
Numerical Methods
scaling
Surface Growth
Scaling Exponent
Cumulants
Particle System
Discrete-time Systems
flux (rate)
Entire Function
Accessibility
Continuous Time
Entire
exponents
Verify

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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title = "Numerical method for accessing the universal scaling function for a multiparticle discrete time asymmetric exclusion process",
abstract = "In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz's original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N→) of a single-particle discrete time system, even in the case of very small system sizes (N≤22). This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP.",
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