Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-05-19
Philosophical Magazine 91, (2011) 1987-1997
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1080/14786435.2010.536179
We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed L\'evy glasses. We introduce a geometric parameter $\alpha$ which plays a role analogous to the exponent characterizing the step length distribution in random systems. We study the large-time behavior of both local and average observables; for the latter case, we distinguish two different types of averages, respectively over the set of all initial sites and over the scattering sites only. The "single long jump approximation" is applied to analytically determine the different asymptotic behaviours as a function of $\alpha$ and to understand their origin. We also discuss the possibility that the root of the mean square displacement and the characteristic length of the walker distribution may grow according to different power laws; this anomalous behaviour is typical of processes characterized by L\'evy statistics and here, in particular, it is shown to influence average quantities.
Burioni Raffaella
Caniparoli L.
Lepri Stefano
Vezzani Alberto
No associations
LandOfFree
Local and average behavior in inhomogeneous superdiffusive media does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Local and average behavior in inhomogeneous superdiffusive media, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local and average behavior in inhomogeneous superdiffusive media will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-479180