Collision densities and mean residence times for $d$-dimensional exponential flights

Details Collision densities and mean residence times for $d$-dimensional exponential flights Collision densities and mean residence times for $d$-dimensional exponential flights

2010-11-17

arxiv.org/abs/1011.4002v3

Phys. Rev. E 83, 041137 (2011)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 5 figures

Scientific paper

10.1103/PhysRevE.83.041137

In this paper we analyze some aspects of {\em exponential flights}, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical/biological species migration, or electron motion. We introduce a general framework for $d$-dimensional setups, and emphasize that exponential flights represent a deceivingly simple system, where in most cases closed-form formulas can hardly be obtained. We derive a number of novel exact (where possible) or asymptotic results, among which the stationary probability density for 2d systems, a long-standing issue in Physics, and the mean residence time in a given volume. Bounded or unbounded, as well as scattering or absorbing domains are examined, and Monte Carlo simulations are performed so as to support our findings.

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