Collision number statistics for transport processes

Abstract

Many physical observables can be represented as a particle spending some random time within a given domain. For a broad class of transport-dominated processes, we detail how it is possible to express the moments of the number of particle collisions in an arbitrary volume in terms of repeated convolutions of the ensemble equilibrium distribution. This approach is shown to generalize the celebrated Kac formula for the moments of residence times, which is recovered in the diffusion limit. Some practical applications are illustrated for bounded, unbounded and absorbing domains.

4 pages, 4 figures

References in corpus (3)

• First-passage times in complex scale-invariant media
• Asymptotic behavior of self-affine processes in semi-infinite domains
• Collision densities and mean residence times for $d$-dimensional exponential flights