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Related Experiment Video

Updated: May 29, 2025

Observation and Analysis of Blinking Surface-enhanced Raman Scattering
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Asymmetric Simple Exclusion Process on the Percolation Cluster: Waiting Time Distribution in Side Branches.

Chandrashekar Iyer1, Mustansir Barma1, Hunnervir Singh2

  • 1Tata Institute of Fundamental Research, 36/P, Gopanpally, Hyderabad 500046, India.

Physical Review Letters
|February 6, 2025
PubMed
Summary
This summary is machine-generated.

We studied particle transport on disordered media using the asymmetric simple exclusion process (ASEP). Long waiting times in side branches lead to dynamical heterogeneity, with particles showing varied mobility.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • The asymmetric simple exclusion process (ASEP) models interacting particles in disordered media.
  • Understanding particle dynamics on complex structures like percolation clusters is crucial.

Purpose of the Study:

  • Investigate the waiting time distribution of particles in side branches of a percolation cluster under ASEP.
  • Analyze the impact of bias field on particle waiting times and system dynamics.

Main Methods:

  • Exact numerical evaluation of waiting time distributions on single side branches.
  • Extension of results to regular comb structures and percolation clusters.
  • Analysis of the steady-state fractional number of particles in side branches.

Main Results:

  • For large bias fields, log(waiting time) distributions exhibit multiple peaks.
  • The fractional number of particles in side branches for time T_w scales as exp(-c*sqrt(log T_w)).
  • Long timescales observed are not reflected in the Markov evolution matrix spectrum.

Conclusions:

  • The ASEP on percolation clusters displays dynamical heterogeneity.
  • Particles segregate into regions of high and low mobility due to complex waiting time distributions.
  • The model provides insights into transport phenomena in disordered systems.