Spatial Persistence of Fluctuating Interfaces

Details Spatial Persistence of Fluctuating Interfaces Spatial Persistence of Fluctuating Interfaces

2000-09-28

arxiv.org/abs/cond-mat/0009439v2

Phys. Rev. Lett. 86, 3700 (2001)

Physics

Condensed Matter

Statistical Mechanics

5 pages, new material added

Scientific paper

10.1103/PhysRevLett.86.3700

We show that the probability, P_0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P_0(l) \sim l^(-\theta). Here \theta is a `spatial' persistence exponent, and takes different values, \theta_s or \theta_0, depending on how the point from which l is measured is specified. While \theta_s is related to fractional Brownian motion, and can be determined exactly, \theta_0 is non-trivial even for Gaussian interfaces.

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