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Summary
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This study explores the slow-bond (SB) problem in the one-dimensional totally asymmetric simple exclusion process (TASEP) with modified hopping rates. Findings reveal how particle interactions and condensation influence jamming and phase separation in driven flow systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • The one-dimensional totally asymmetric simple exclusion process (TASEP) exhibits jamming and phase separation due to slow-bond (SB) defects.
  • Finite-size effects can lead to crossover scaling behaviors in the 1D TASEP.

Purpose of the Study:

  • To investigate whether particle interactions can render the SB defect irrelevant in the 1D TASEP.
  • To explore the interplay between jamming and condensation phenomena in modified TASEP models.
  • To analyze the current-density relation and phase diagrams under modified hopping rates.

Main Methods:

  • Modification of TASEP hopping rates based on particle interaction and proximity.
  • Application of the condensation concept from the zero-range process.
  • Mean-field calculations for fundamental and phase diagrams.
  • Numerical verification of theoretical predictions.

Main Results:

  • The modified TASEP hopping rate incorporates interaction parameters and nearest-neighbor distances.
  • A detailed analysis of the interplay between jamming and condensation in the current-density relation is presented.
  • Mean-field calculations yield fundamental and phase diagrams for the modified SB problem.
  • Condensation of holes was found to suppress particle jamming, and vice versa.

Conclusions:

  • Particle interactions can significantly alter the behavior of the SB problem in 1D TASEP.
  • The interplay between jamming and condensation leads to novel phase behaviors, particularly in partially condensed phases.
  • The study provides insights into the fundamental diagram and phase diagram of driven particle systems with modified dynamics.