Abstract
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.
- Received 5 June 2003
DOI:https://doi.org/10.1103/PhysRevLett.91.160601
©2003 American Physical Society