Dynamic critical behavior of the Landau-Peierls fluctuations:: Scaling form of the dynamic density autocorrelation function for smectic-A films

In this paper, we study the dynamic density autocorrelation function G(r,t) for smectic-A films in the layer sliding geometry. We first postulate a scaling form for G, and then we shaw that our postulated scaling form holds by comparing the scaling predictions with detailed numerical calculations. We find some deviations from the scaling form only for very thin films. For thick films, we find a region of a bulklike behavior, where the dynamics is characterized by the same static critical exponent eta, which was originally introduced by Caille [C. R. Acad. Sci. Ser. B 274 891 (1972)]. In the limit of very large distance perpendicular to the layer normal, or in the limit of very long time, we find that the decay of G is governed by the surface exponent chi = k(B)Tq(z)(2)/(4 pi gamma), where gamma is the surface tension and the wave-vector component q(2) satisfies the Bragg condition. We also find an intermediate perpendicular distance regime in which the decay of C is governed by the time-dependent exponent chi exp(-t/tau(0)), where the relaxation time is given by tau(0) = eta(3)(Ld)/(2 gamma), where eta(3) is the layer sliding viscosity, and Ld is the film thickness. [S1063-651X(99)03403-0].