The effect of asymmetric disorder on the diffusion on arbitrary networks

Details The effect of asymmetric disorder on the diffusion on arbitrary networks The effect of asymmetric disorder on the diffusion on arbitrary networks

2012-03-08

arxiv.org/abs/1203.1735v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

Considering diffusion in the presence of asymmetric disorder, an exact relationship between the strength of weak disorder and electric resistance is established, which is valid on arbitrary networks. Accordingly, the law of diffusion is stable against weak asymmetric disorder if the resistance exponent $\zeta$ of the network is negative. In case of $\zeta>0$, numerical analyses of the mean first-passage time $\tau$ on various fractal lattices show that the logarithmic scaling of $\tau$ with the distance $l$, $\ln\tau\sim l^{\psi}$, is a general rule with a dynamical exponent $\psi$ that is characteristic of the underlying lattice.

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