Phys. Rev. Lett. 91, 160601 (2003) [4 pages]Exact Dynamics of a Continuous Time Random Walker in the Presence of a Boundary: Beyond the Intuitive Boundary Condition ApproachReceived 5 June 2003; published 13 October 2003 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. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.91.160601
DOI:
10.1103/PhysRevLett.91.160601
PACS:
05.40.–a, 82.20.–w
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