Efficiency of encounter-controlled reaction between diffusing reactnats in a finite lattice

摘要

Numberically-exact values of the mean walk length befre first encoiunter for reactants diffusing on a lattice are calculated by generalizing a Markovian method introduced pereviously. The approach developed is illustrated by presenting results for two random walkers diffusing simulataneously on a square-planar lattice;the results obtained are compared with those calcualted assuming one of the reactant partners is stationary.In almost all cases, it is found that the former process is the more efficient. Analytic arguments are presented and Monte Carlo studies are carried out to support the results obtained.