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Persistence exponents for fluctuating interfaces | | J. Krug
; H. Kallabis
; S.N. Majumdar
; S.J Cornell
; A.J. Bray
; C. Sire
; | | Date: |
29 Apr 1997 | | Journal: | Phys. Rev. E 56 (1997) 2702 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | Universitaet Essen HLRZ, Juelich Tata Institute, Bombay Manchester University CNRS, Universite Toulouse | | Abstract: | Numerical and analytic results for the exponent heta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic roughness exponent eta, with 0 < eta < 1; for eta = 1/2 the time evolution is Markovian. Using simulations of solid-on-solid models, of the discretized continuum equations as well as of the associated zero-dimensional stationary Gaussian process, we address two problems: The return of an initially flat interface, and the return to an initial state with fully developed steady state roughness. The two problems are shown to be governed by different exponents. For the steady state case we point out the equivalence to fractional Brownian motion, which has a return exponent heta_S = 1 - eta. The exponent heta_0 for the flat initial condition appears to be nontrivial. We prove that heta_0 o infty for eta o 0, heta_0 geq heta_S for eta < 1/2 and heta_0 leq heta_S for eta > 1/2, and calculate heta_{0,S} perturbatively to first order in an expansion around the Markovian case eta = 1/2. Using the exact result heta_S = 1 - eta, accurate upper and lower bounds on heta_0 can be derived which show, in particular, that heta_0 geq (1 - eta)^2/eta for small eta. | | Source: | arXiv, cond-mat/9704238 | | Services: | Forum | Review | PDF | Favorites | |
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