Relation between a system described by a simplified Muriel kinetic equation and a kicked system with a Mittag-Leffler waiting time distribution between kicks

Abstract

We point out that the time-evolved momentum distribution function obtained by solving a simplified Muriel kinetic equation for a kicked two-level system is identical to that obtained from a kicked system with exponential waiting time distribution between kicks (i.e. the number of kicks, N, a particle has received by time t is a Poisson renewal process). We then obtain the evolution of the momentum distribution function for a kicked-system with a Mittag-Leffler waiting time distribution between kicks.