Anomalous Roughness, Localization, and Globally Constrained Random Walks

Details Anomalous Roughness, Localization, and Globally Constrained Random Walks Anomalous Roughness, Localization, and Globally Constrained Random Walks

2001-03-27

arxiv.org/abs/cond-mat/0103549v2

Phys. Rev. E 64, 046131 (2001)

Physics

Condensed Matter

Statistical Mechanics

15 pages

Scientific paper

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.

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