1ST-PASSAGE TIMES AND SURVIVAL PROBABILITIES FOR PARTICLES MOVING IN A FIELD OF RANDOM CORRELATED FORCES

Generalized diffusion equations for the density of a particle moving i n one dimension under the influence of Gaussian noise, with Ornstein-U hlenbeck correlations, are used to study first-passage times and survi val probabilities in the presence of static traps. These diffusion equ ations have been derived for times that are either short or large comp ared to the correlation time tau and are used, in particular, near tau = 0 (limit of quasiperfect dynamic randomness) and near tau = infinit y (limit of quasistatic randomness). The mean first-passage times scal e with distance and with model parameters in the same way as do superd iffusion times derived from mean-square displacements. The long-time s urvival probability decays exponentially in the tau-->0 case and decay s as a shrunk exponential, with an exponent t 4/3, for quasistatic for ces. The short-time behavior of the survival probability, as well as t he finite-tau corrections near tau = 0 and near tau = infinity, are al so analyzed.