Particle transport with branching in a medium randomly varying in time

摘要

The theory of particle transport with branching in a medium randomly varying in time is developed in this paper. We consider an evolution equation for the probability distribution of the number of particles in a multiplying system whose properties jump randomly between two discrete states. A forward type master equation is derived for the probability distributions, and from these, the first two factorial moments are calculated, including the variance. This model can be considered the unification of stochastic methods that were used either for the particle fluctuations in a constant multiplying medium via the master equation technique, or in a fluctuating medium via the Langevin technique. The results obtain show a much richer variety of behaviour than any of the above two methods separately can reconstruct.