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We show that the dynamics of disordered charge density waves (CDWs) and spindensity waves (SDWs) is a collective phenomenon. The very low temperaturespecific heat relaxation experiments are characterized by: (i) ``interrupted''ageing (meaning that there is a maximal relaxation time); and (ii) a broadpower-law spectrum of relaxation times which is the signature of a collectivephenomenon. We propose a random energy model that can reproduce these twoobservations and from which it is possible to obtain an estimate of the glasscross-over temperature (typically $T_g \simeq 100 - 200$ mK). The broadrelaxation time spectrum can also be obtained from the solutions of twomicroscopic models involving randomly distributed solitons. The collectivebehavior is similar to domain growth dynamics in the presence of disorder andcan be described by the dynamical renormalization group that was proposedrecently for the one dimensional random field Ising model [D.S. Fisher, P. LeDoussal and C. Monthus, Phys. Rev. Lett. {\bf 80}, 3539 (1998)]. The typicalrelaxation time scales like $\tau^{\rm typ} \sim \tau_0 \exp{(T_g/T)}$. Theglass cross-over temperature $T_g$ related to correlations among solitons isequal to the average energy barrier and scales like $T_g \sim 2 x \xi_0\Delta$. $x$ is the concentration of defects, $\xi_0$ the correlation length ofthe CDW or SDW and $\Delta$ the charge or spin gap.Comment: 20 pages, 16 figure

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons