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First-passage times and survival probabilities for particles moving in a field of random correlated forces
Phys. Rev. E 48, 2397 – Published 1 October, 1993
DOI: https://doi.org/10.1103/PhysRevE.48.2397
Abstract
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 τ and are used, in particular, near τ=0 (limit of quasiperfect dynamic randomness) and near τ=∞ (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 τ→0 case and decays as a shrunk exponential, with an exponent , for quasistatic forces. The short-time behavior of the survival probability, as well as the finite-τ corrections near τ=0 and near τ=∞, are also analyzed.
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