Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions.

Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this Letter we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaymé-Galton-Watson process describing the statistics of the number of clusters. Our work has concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.

Universal Scaling of the Velocity Field in Crack Front Propagation.

The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are, however, difficult to characterize in experiments at a finite drive. Here, we show that the correlation functions of the velocity field along the front allow us to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient, and can be extended to all systems displaying avalanche dynamics.

Geometrical dependence of quantum decoherence in circular arenas with side-wires.

Low-temperature quantum phase coherence lengths were experimentally measured in mesoscopic circular arenas fabricated on InGaAs quantum wells. The arenas are connected to wide sample regions by short side-wires, to investigate the effects of geometry in comparison to intrinsic materials properties on quantum decoherence. Universal conductance fluctuations were used to quantify the phase coherence lengths as a function of temperature and geometry. The experimental data show a dependence of phase coherence lengths on side-wire length and width-to-length ratio, which is accounted for by the competing effects of decoherence by coupling to the classical environment and Nyquist decoherence in ergodic wires. The observed decay of phase coherence lengths with the increasing temperature is consistent with expectations. The work demonstrates that geometrical effects influence the measured mesoscopic quantum decoherence.