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Exact tagged particle correlations in the random average process.

R Rajesh1, S N Majumdar

  • 1Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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In the random average process, tracer particle movement shows subdiffusive behavior without bias and diffusive behavior with bias. Analytical calculations reveal exact scaling functions for these correlated particle position dynamics.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • The random average process is a fundamental interacting particle system in one dimension.
  • Understanding particle correlations is crucial for characterizing system dynamics.

Purpose of the Study:

  • To analytically investigate correlations between tagged particle positions in the random average process.
  • To determine the impact of external bias on particle fluctuations and correlations.

Main Methods:

  • Analytical techniques were employed to study the system in steady state.
  • Exact computation of scaling functions and prefactors for particle fluctuations.

Main Results:

  • Mean-squared autofluctuation of a tracer particle exhibits subdiffusive growth (t^1/2) without bias and diffusive growth (t) with bias.

Related Experiment Videos

  • The external bias significantly alters the time dependence of the mean-squared fluctuation between two tagged particles.
  • Exact scaling functions describing crossovers and prefactors were determined.

    • Conclusions:

    • The study provides exact analytical results for particle correlations in the random average process.
    • External bias plays a critical role in modulating the diffusive and subdiffusive behaviors of particles.
    • Comparison with the simple exclusion process highlights unique aspects of the random average model.