Exact dynamics of a continuous time random walker in the presence of a boundary: beyond the intuitive boundary condition approach.
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.
Sung
Jaeyoung
J
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Silbey
Robert J
RJ