Persistence of Kardar-Parisi-Zhang interfaces
Center for Polymer Studies, Boston University - Boston, MA 02215, USA
2 Höchstleistungsrechenzentrum, Forschungszentrum Jülich - 52425 Jülich, Germany
3 Fachbereich Physik, Universität GH Essen, D-45117 Essen, Germany
Accepted: 5 November 1998
The probabilities that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval are shown numerically to decay as with and . Bounds on are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent for a d–dimensional interface with roughness and dynamic exponents β and z is conjectured to be . For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.
PACS: 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 81.10.Aj – Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, 1999