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Liang Luo1, Lei-Han Tang1,2

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|November 14, 2015
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Summary
This summary is machine-generated.

We propose an approximate expression for first-passage-time (FPT) distribution in quenched random trap models. This theory explains sample-to-sample variations and confirms two time scales in particle diffusion.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Particle diffusion in disordered media is often modeled using continuous-time random walks.
  • Quenched random traps introduce complexities not fully captured by annealed models.

Purpose of the Study:

  • To develop an approximate expression for first-passage-time (FPT) distribution in quenched random trap models.
  • To enable detailed comparison between quenched and annealed random walk models.
  • To investigate sample-to-sample variations in FPT statistics for finite-sized systems.

Main Methods:

  • Theoretical derivation of an approximate FPT distribution expression.
  • Numerical simulations of a quenched trap model with power-law sojourn times.

Main Results:

  • The proposed expression allows for direct comparison of quenched and annealed random walks.
  • Deep trap characteristics significantly influence FPT statistics in finite systems.
  • Simulations confirm two characteristic time scales and a non-self-averaging FPT distribution.

Conclusions:

  • The theory accurately predicts key features of particle diffusion in quenched random trap systems.
  • Understanding trap dynamics is crucial for characterizing diffusion processes.
  • The findings highlight the limitations of averaged descriptions for disordered systems.