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Related Experiment Videos

Local and occupation time of a particle diffusing in a random medium.

Satya N Majumdar1, Alain Comtet

  • 1Laboratoire de Physique Quantique (UMR C5626 du CNRS), Université Paul Sabatier, 31062 Toulouse Cedex, France.

Physical Review Letters
|August 23, 2002
PubMed
Summary

We analyzed particle motion in a one-dimensional potential with deterministic and random parts. Introducing quenched randomness drastically alters probability distributions, causing loss of self-averaging and significant fluctuations.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • Particles in one-dimensional potentials are fundamental models.
  • Understanding local and occupation times is crucial for analyzing particle dynamics.
  • Quenched randomness introduces disorder, significantly impacting system behavior.

Purpose of the Study:

  • To analytically investigate probability distributions of local and occupation times for a particle in a mixed potential.
  • To compare behaviors with and without quenched randomness.
  • To characterize the impact of quenched disorder on statistical properties.

Main Methods:

  • Analytical treatment of probability distributions.
  • Analysis of local time and occupation time within a time window.

Related Experiment Videos

  • Comparison of asymptotic behaviors under different potential configurations.

    • Main Results:

    • In the absence of randomness, distributions exhibit three distinct asymptotic behaviors based on the deterministic potential (unstable, stable, flat).
    • The introduction of quenched randomness drastically modifies these distributions.
    • Loss of self-averaging and wide sample-to-sample fluctuations are observed due to quenched disorder.

    Conclusions:

    • Quenched randomness fundamentally alters the statistical properties of particle dynamics.
    • The presence of disorder leads to non-self-averaging behavior and increased variability.
    • This study highlights the significant impact of quenched disorder on fundamental physical observables.