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From quenched disorder to continuous time random walk.

Stanislav Burov1

  • 1Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel.

Physical Review. E
|January 20, 2018
PubMed
Summary

This study presents a quantitative method for transport in disordered systems. We map the quenched trap model to continuous time random walks, providing exact expressions for diffusion and drift.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Transport phenomena in disordered systems are crucial for understanding various physical and chemical processes.
  • Quenched disorder introduces complexities that traditional random walk models struggle to capture.
  • Subdiffusive transport is a common characteristic in such systems.

Purpose of the Study:

  • To develop a quantitative representation for transport in systems with quenched disorder.
  • To establish an explicit mapping between the quenched trap model and continuous time random walks.
  • To derive analytical expressions for key transport parameters.

Main Methods:

  • Utilizing a linear temporal transformation (t→t/Λ^{1/α}) for transient processes in the subdiffusive regime.

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  • Establishing an exact form for the constant Λ^{1/α}.
  • Obtaining the disorder-averaged position probability density function.

    • Main Results:

    • An asymptotic mapping of the quenched trap model to continuous time random walks is achieved.
    • The constant Λ^{1/α} is determined exactly.
    • Analytic expressions for the diffusion coefficient and drift in the quenched trap model are derived.

    Conclusions:

    • The developed mapping provides a powerful tool for analyzing transport in disordered media.
    • The derived analytical expressions offer precise quantitative insights into system dynamics.
    • This work advances the understanding of subdiffusive transport under quenched disorder.