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Asymmetric exclusion process with global hopping.

Chikashi Arita1, Jérémie Bouttier, P L Krapivsky

  • 1Institut de Physique Théorique, IPhT, CEA Saclay and URA 2306, CNRS, 91191 Gif-sur-Yvette Cedex, France and Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany.

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Summary
This summary is machine-generated.

This study investigates a modified exclusion process with a special site enabling long-range particle movement. A nonequilibrium phase transition occurs, forming a shock wave in the system

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • The totally asymmetric simple exclusion process (TASEP) is a fundamental model in statistical mechanics.
  • Understanding non-equilibrium phase transitions is crucial for complex systems.
  • Previous models often assume local particle interactions.

Purpose of the Study:

  • To analyze a one-dimensional totally asymmetric simple exclusion process (TASEP) with a unique long-range particle interaction.
  • To identify and characterize the nonequilibrium phase transition in this modified TASEP.
  • To investigate the emergent phenomena, such as shock wave formation.

Main Methods:

  • Theoretical analysis of the one-dimensional totally asymmetric simple exclusion process (TASEP).
  • Investigation of the system's stationary state and density profile.
  • Identification of critical density and phase transition behavior.

Main Results:

  • The modified TASEP achieves a nontrivial stationary state with a spatially varying density profile.
  • A nonequilibrium phase transition is observed at a critical average density of approximately 0.185.
  • Exceeding the critical density leads to the formation of a shock wave in the bulk, in addition to a discontinuity near the special site.

Conclusions:

  • The introduction of a special site with long-range particle ejection significantly alters the TASEP dynamics.
  • The system exhibits a distinct nonequilibrium phase transition characterized by shock wave formation.
  • This model provides insights into non-equilibrium phenomena in systems with long-range interactions.