Persistence of Kardar-Parisi-Zhang Interfaces

Abstract

The probabilities $P_{\pm }(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0,t)$ are shown numerically to decay as $P_{\pm }\sim (t_0/t{)}^{{\theta }_{\pm }}$ with ${\theta }_{+}=1.18\pm 0.08$ and ${\theta }_{-}=1.64\pm 0.08$. Bounds on ${\theta }_{\pm }$ are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent $\bar{\lambda }$ for a $d$--dimensional interface with roughness and dynamic exponents $\beta$ and $z$ is conjectured to be $\bar{\lambda }=\beta +d/z$. For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.

4 pages, 3 figures, uses revtex and psfig

References in corpus (1)

• Exact Large Deviation Function in the Asymmetric Exclusion Process

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