On mean residence and first passage times in finite one-dimensional systems

We present a simple derivation of mean residence times (MRTs) and mean first passage times (MFPTs) for random walks in finite one-dimensional systems. The derivation is based on the analysis of the inverse matrix of transition rates which represents the random walk rate equations. The dependence of the MRT and of the MFPT on the initial condition, on the system size, and on the elementary rates is studied and a relationship to stationary solutions is established. Applications to models of light harvesting by supermolecules, and of random barriers, and to relaxation in the Ehrenfest model are discussed in detail. We propose a way to control the MFPT in supermolecules, such as dendrimers, via molecular architecture.

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