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Exact probability function for bulk density and current in the asymmetric exclusion process.

Martin Depken1, Robin Stinchcombe

  • 1University of Oxford, Department of Physics, Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom. depken@lorentz.leidenuniv.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary
This summary is machine-generated.

We studied the asymmetric simple exclusion process with open boundaries, finding a non-Gaussian distribution for bulk density and current. Fluctuations in current are continuous, while density fluctuations are discontinuous at phase transitions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Non-equilibrium Systems

Background:

  • The asymmetric simple exclusion process (ASEP) is a key model for driven diffusive systems.
  • It exhibits a nonequilibrium steady-state transition, crucial for understanding complex systems.
  • Previous reports on ASEP with open boundaries were brief.

Purpose of the Study:

  • To provide a full derivation of the joint probability function for bulk density and current in ASEP with open boundaries.
  • To analyze the nature of fluctuations at phase transitions.
  • To present a simplified method for calculating the normalization constant.

Main Methods:

  • Utilizing standard operator algebraic techniques.
  • Introducing a modified operator algebra.
  • Deriving exact forms for the joint probability function in both finite and thermodynamic limits.

Main Results:

  • An exact, non-Gaussian joint probability function for bulk density and current was derived.
  • Density fluctuations exhibit discontinuity, while current fluctuations are continuous at phase transitions.
  • A simplified method for calculating the normalization constant was developed.

Conclusions:

  • The normalization constant, analogous to the partition function, fully characterizes fluctuations in ASEP.
  • The study offers a comprehensive understanding of ASEP steady-state properties.
  • New insights into the behavior of driven diffusive systems were provided.