Theory and simulation of multiple-trapping transport through a finite slab

The theory of the multiple-trapping model for dispersive transport is fomulated for the case of a continuous distribution of trapping levels. The density of particles and the current are expressed in terms of the waiting-time distribution for release. Numerical simulations of the multiple-trapping model are performed for an exponential distribution of trapping levels and complete agreement with the theoretical expressions is found. The apparent exponent of the power-law behavior of the current in the drift and extraction regimes are investigated. The exponents in the extraction regime approaches the scaling prediction only asymptotically, at very long times, except around one particluar value. Results for the time-dependent energy distribution of the trapped particles are also given.