Localization length exponent in quantum percolation

How the site degree influences quantum probability on inhomogeneous substrates

We investigate the effect of the node degree and energy E on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependency of the quantum probability for each site on its degree. For a class of biregular structures formed by two disjoint subsets of sites sharing the same degree, the probability P_{k}(E) of finding the electron on any site with k neighbors is independent of E≠0, a consequence of an exact analytical result that we prove for any bipartite lattice. For more general nonbipartite structures, P_{k}(E) may depend on E as illustrated by an exact evaluation of a one-dimensional semiregular lattice: P_{k}(E) is large for small values of E when k is also small, and its maximum values shift towards large values of |E| with increasing k. Numerical evaluations of P_{k}(E) for two different types of percolation clusters and the Apollonian network suggest that this observed feature might be generally valid.

Spatial coherence in complex photonic and plasmonic systems

The concept of cross density of states characterizes the intrinsic spatial coherence of complex photonic or plasmonic systems, independently of the illumination conditions. Using this tool and the associated intrinsic coherence length, we demonstrate unambiguously the spatial squeezing of eigenmodes on disordered fractal metallic films, thus clarifying a basic issue in plasmonics.

Double exchange model for magnetic hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu1-xCaxB6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as the Hall effect, magnetoresistance, frequency dependent conductivity, and dc resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature T(C) as a function of the plasma frequency omega(p).

Failure due to fatigue in fiber bundles and solids

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold (sigma(c)) beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress sigma. We solve this dynamics of failure analytically and show that the average failure time tau of the bundle decreases exponentially as sigma-->sigma(c) from below and tau=0 for sigma>or=sigma(c). We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of the Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress sigma less than the bundle's strength sigma(c); (beyond which it fails instantly). The average failure time tau is again seen to decrease exponentially as sigma-->sigma(c); from below and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.