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Anomalous roughness, localization, and globally constrained random walks.

J Dong Noh1, H Park, D Kim

  • 1Department of Physics, Inha University, Inchon 402-751, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
Summary

We analyzed random walks with an even-visit constraint, finding a dynamic exponent of z=d+2. This explains anomalous surface roughness in 1D systems with specific surface dynamics.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Surface Science

Background:

  • Random walks are fundamental models in physics.
  • Surface dynamics and scaling properties are crucial for understanding materials.
  • Electron localization is a key phenomenon in disordered systems.

Purpose of the Study:

  • To determine the scaling properties of constrained random walks.
  • To connect these walks to surface dynamics and electron localization models.
  • To analytically derive the dynamic exponent and explain observed roughness.

Main Methods:

  • Analysis of random walker scaling properties with an even-visit constraint.
  • Mapping to unconstrained random walks on random surfaces.
  • Connection to non-Hermitian random free fermion models.

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Main Results:

  • The dynamic exponent was found to be z=d+2 in spatial dimension d.
  • Anomalous surface roughness with exponent alpha=1/3 in 1D systems was explained.
  • The model relates constrained random walks to electron localization phenomena.

Conclusions:

  • The study provides a theoretical framework for understanding constrained random walks.
  • The findings elucidate the relationship between surface dynamics, random walks, and electron localization.
  • The derived dynamic exponent offers insights into anomalous scaling in physical systems.