  Taking one-dimensional random transverse Ising model (RTIM) with the
double-Gaussian disorder for example, we investigated the spin autocorrelation
function (SAF) and associated spectral density at high temperature by the
recursion method. Based on the first twelve recurrants obtained analytically,
we have found strong numerical evidence for the long-time tail in the SAF of a
single spin. Numerical results indicate that when the standard deviation
{\sigma}_{JS} (or {\sigma}_{BS}) of the exchange couplings J_{i} (or the random
transverse fields B_{i}) is small, no long-time tail appears in the SAF. The
spin system undergoes a crossover from a central-peak behavior to a
collective-mode behavior, which is the dynamical characteristics of RTIM with
the bimodal disorder. However, when the standard deviation is large enough, the
system exhibits similar dynamics behaviors to those of the RTIM with the
Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior
for large {\sigma}_{JS} or a disordered behavior for large {\sigma}_{BS}. In
this instance, the long-time tails in the SAFs appear, i.e., C(t)\simt^{-2}.
Similar properties are obtained when the random variables (J_{i} or B_{i})
satisfy other distributions such as the double-exponential distribution and the
double-uniform distribution.
