Thermally activated particle motion in disordered media is very sensitive to the form of the tail of the probability distribution of the potential barriers. I evaluate this distribution tail by using the optimal fluctuation method. For short-correlated quenched Gaussian disorder potentials with monotone decreasing covariances I reproduce the potential barrier distribution tail obtained by Lopatin and Vinokur [1]. However, for nonmonotonic covariances which exhibit negative correlations, I show that the potential barrier distribution tail is higher. This leads to an exponential increase of the mean escape time of the particles. The transition between the two regimes has the character of a first-order transition. These results are published in Ref. [2].
[1] A. V. Lopatin and V. M. Vinokur, Phys. Rev. Lett. 86, 1817 (2001).
[2] B. Meerson, Phys. Rev. E 105, 034106 (2022),