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The Dynamics of Partially Pinned Random Systems: A Computer Simulation

Numerical simulations are reported on a one-dimensional randomly pinned system below the depinning transition. The time-dependent polarization obeys a stretched exponential P(t) = P0[1 - exp [-(t/t0)α]] with α < 1. Metastable states and remanent polarization also follow from the model which reproduces many recent observations made on pinned charge density waves. The model leads to critically divergent P0 and t0 as the system approaches the depinning transition.