Year: 2001
Type: article
Abstract: 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 ${P}_{0}(l)\ensuremath{\sim}{l}^{\ensuremath{-}\ensuremath{\theta}}$. Here $\ensuremath{\theta}$ is a ``spatial'' persistence exponent, and takes different values, ${\ensuremath{\theta}}_{s}$ or ${\ensuremath{\theta}}_{0}$, depending on how the point from which $l$ is measured is specified. These exponents are shown to map onto corresponding temporal persistence exponents for a generalized $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ random-walk equation. The exponent ${\ensuremath{\theta}}_{0}$ is nontrivial even for Gaussian interfaces.
Source: Physical Review Letters
Authors: Satya N. Majumdar, Alan J. Bray
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2013275669