Dynamic critical behavior of the Landau-Peierls fluctuations: Scaling formof 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 sc aling form for G, and then we shaw that our postulated scaling form holds b y comparing the scaling predictions with detailed numerical calculations. W e 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 original ly introduced by Caille [C. R. Acad. Sci. Ser. B 274 891 (1972)]. In the li mit of very large distance perpendicular to the layer normal, or in the lim it of very long time, we find that the decay of G is governed by the surfac e exponent chi = k(B)Tq(z)(2)/(4 pi gamma), where gamma is the surface tens ion and the wave-vector component q(2) satisfies the Bragg condition. We al so 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].