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 in one dimension under the influence of Gaussian noise, with Ornstein-Uhlenbeck correlations, are used to study first-passage times and survival probabilities in the presence of static traps. These diffusion equations have been derived for times that are either short or large compared to the correlation time tau and are used, in particular, near tau = 0 (limit of quasiperfect dynamic randomness) and near tau = infinity (limit of quasistatic randomness). The mean first-passage times scale with distance and with model parameters in the same way as do superdiffusion times derived from mean-square displacements. The long-time survival probability decays exponentially in the tau-->0 case and decays as a shrunk exponential, with an exponent t 4/3, for quasistatic forces. The short-time behavior of the survival probability, as well as the finite-tau corrections near tau = 0 and near tau = infinity, are also analyzed.