Anomalous Roughness, Localization, and Globally Constrained Random Walks

Abstract

The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are subject to dissociative dimer-type surface dynamics. Moreover, they can be mapped onto unconstrained random walks on a random surface, and the latter corresponds to a non-Hermitian random free fermion model which describes electron localization near a band edge. We show analytically that the dynamic exponent of this random walk is $z=d+2$ in spatial dimension $d$. This explains the anomalous roughness, with exponent $\alpha =1/3$, in one dimensional equilibrium surfaces with dissociative dimer-type dynamics.

15 pages

Cited by in corpus (8)

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• Dynamical surface structures in multi-particle-correlated surface growths
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• Non-universal dynamics of dimer growing interfaces
• Scaling and width distributions of parity conserving interfaces
• Roughening of $k$-mer growing interfaces in stationary regimes