Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps

Abstract

We calculate the survival probability P_S(t) up to time t of a tracer particle moving along a deterministic trajectory in a continuous d-dimensional space in the presence of diffusing but mutually noninteracting traps. In particular, for a tracer particle moving ballistically with a constant velocity c, we obtain an exact expression for P_S(t), valid for all t, for d<2. For d \geq 2, we obtain the leading asymptotic behavior of P_S(t) for large t. In all cases, P_S(t) decays exponentially for large t, P_S(t) \sim \exp(-θt). We provide an explicit exact expression for the exponent θin dimensions d \leq 2, and for the physically relevant case, d=3, as a function of the system parameters.