Closed-form solutions for continuous time random walks on finite chains

Details Closed-form solutions for continuous time random walks on finite chains Closed-form solutions for continuous time random walks on finite chains

2007-02-23

arxiv.org/abs/cond-mat/0702561v1

Phys. Rev. Lett. 95, 098105 (2005)

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1103/PhysRevLett.95.098105

Continuous time random walks (CTRW) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation (GME). Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formulae, an escape problem from a biased chain is considered.

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