Exact Results in Trapping Reactions for Mobile Particles and a Single Trap
We have exploited a stochastic model for the description of diffusion controlled reactions for trapping processes with a single trap in a one-dimensional lattice, in order to describe in an exact way the particle distribution as seen from the trap, being it fix or mobile, as well as for perfect or imperfect reactions. From this we obtain the exact result for the total number of absorbed particles. Moreover we get a formal expression for the nearest-neighbor-particle distribution that gives the known results in the limit cases of fixed trap and fixed particles.
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