Target annihilation by diffusing particles in inhomogeneous geometries

Details Target annihilation by diffusing particles in inhomogeneous geometries Target annihilation by diffusing particles in inhomogeneous geometries

2009-09-03

arxiv.org/abs/0909.0773v1

PHYSICAL REVIEW E 80, 030107R (2009)

Physics

Condensed Matter

Statistical Mechanics

To appear in Physical Review E - Rapid Communications

Scientific paper

10.1103/PhysRevE.80.030107

The survival probability of immobile targets, annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points, as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behaviour at large times can still be expressed in terms of the spectral dimension $\widetilde {d}$, and its exact analytical expression is given. The results show that the asymptotic survival probability is site independent on recurrent structures ($\widetilde{d}\leq2$), while on transient structures ($\widetilde{d}>2$) it can strongly depend on the target position, and such a dependence is explicitly calculated.

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