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Phys Rev Lett. 2003 Oct 17;91(16):160601. Epub 2003 Oct 13.

Exact dynamics of a continuous time random walker in the presence of a boundary: beyond the intuitive boundary condition approach.

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Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.


We derive the exact dynamics of a random walker with arbitrary non-Markovian transport and reaction rate distribution at a boundary, and present exact solutions in the continuum limit. We find that the ultimate escape probability of the particle is independent of the transport mechanism in contradiction to the long-standing belief based on the conventional approach. We also find a phase transition in the relaxation kinetics associated with the heterogeneity of the transport media.

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