  The dynamics of the random-phase sine-Gordon model, which describes 2D
vortex-glass arrays and crystalline surfaces on disordered substrates, is
investigated using the self-consistent Hartree approximation. The
fluctuation-dissipation theorem is violated below the critical temperature T_c
for large time t>t* where t* diverges in the thermodynamic limit. While above
T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it
approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* -
c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On
larger time scales t > t* the dynamics becomes non-ergodic. The static
correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi*
proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x}
where m is approximately T/T_c near T_c, in general agreement with the
variational replica-symmetry breaking approach and with recent simulations of
the disordered-substrate surface. For strong- coupling the transition becomes
first-order.
