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Spatial persistence of fluctuating interfaces.

S N Majumdar1, A J Bray

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

Physical Review Letters
|May 1, 2001
PubMed
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The study reveals how fluctuating interface heights persist over distance, introducing spatial persistence exponents. These exponents connect to temporal persistence in random-walk models, even for Gaussian interfaces.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Surface Science

Background:

  • Fluctuating interfaces are fundamental in various physical systems, from crystal growth to polymer dynamics.
  • Understanding the persistence of interface height is crucial for characterizing their steady-state behavior and statistical properties.

Purpose of the Study:

  • To determine the probability distribution governing the height of fluctuating interfaces in steady state.
  • To introduce and analyze spatial persistence exponents that characterize interface height behavior along linear cuts.
  • To establish a connection between spatial and temporal persistence exponents using random-walk models.

Main Methods:

  • Analytical derivation of the probability P0(l) for an interface height staying above its initial value.

Related Experiment Videos

  • Definition and calculation of spatial persistence exponents (theta(s) and theta(0)) based on measurement point specification.
  • Mapping spatial exponents to temporal persistence exponents for a generalized one-dimensional (d=1) random-walk equation.

    • Main Results:

    • The probability P0(l) decays as a power law, P0(l) ~ l^(-theta), where theta is a spatial persistence exponent.
    • Distinct spatial persistence exponents, theta(s) and theta(0), are identified depending on the reference point for distance l.
    • The exponent theta(0) is shown to be non-trivial even for simple Gaussian interfaces, indicating complex persistence behavior.

    Conclusions:

    • The study quantifies the spatial persistence of fluctuating interface heights using novel exponents.
    • A direct relationship is established between spatial persistence in interfaces and temporal persistence in random walks.
    • The findings offer new insights into the statistical mechanics of interfaces and disordered systems.