Freezing of dynamical exponents in low dimensional random media

A particle in a random potential with logarithmic correlations in dimension s d = 1,2 is shown to undergo a dynamical transition at T-dyn > 0. In d = 1 exact results show T-dyn = T-c, the static glass transition temperature, a nd that the dynamical exponent changes from z(T) = 2 + 2(T-c / T)(2) at hig h T to z(T) = 4T(c) / T in the glass phase. The same formulas are argued to hold in d = 2. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In d = 1 a mapping between dynamics and stat ics is unveiled and freezing involves barriers as well as valleys. Anomalou s scaling occurs in the creep dynamics, relevant to dislocation motion expe riments.