  We consider the one-dimensional Glauber dynamics with coupling disorder in
terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the
spectrum gap of these latter are evaluated numerically by averaging over both
binary and Gaussian disorder realizations. In the first case, these exponents
are found to follow the non-universal values of those of plain dimerized
chains. In the second situation their values are still non-universal and
sub-diffusive below a critical variance above which, however, the relaxation
time is suggested to grow as a stretched exponential of the equilibrium
correlation length.
