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Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as N = ρ/(1 − ρ), and the density increase rate is drastically reduced by a factor e −N . Consequently, a logarithmically slow approach to the final state is found ρ∞ − ρ(t) ∼ = 1/ ln t.

We have studied the voltage fluctuations of current-biased, micron-scale magnetic tunnel junctions. We find that the spectral power density is 1/f-like at low frequencies and becomes frequency independent at high frequencies. The frequency-independent background noise is due to Johnson-Nyquist noise and shot noise mechanisms. The nature of the 1/f noise has its origin in two different mechanisms. In the magnetic hysteresis loops this noise power is strongly field-dependent and is due to thermal magnetization fluctuations in both the ''free'' and ''fixed'' magnetic layers. We attribute these magnetic fluctuations to thermally excited hopping of magnetic domain walls between pinning sites. At high temperatures, this magnetic noise is found to track the dc resistance susceptibility but it is not in quantitative agreement with the fluctuation dissipation relation, indicating that the magnetic structure is not in equilibrium. A second mechanism for the 1/f noise, connected with defects in the tunnel barrier but not related to the overall magnetization fluctuations, was found at fields for which the magnetic structure in the free and fixed layers is well aligned. We attribute this noise to electron trapping processes having thermally activated kinetics and a broad distribution of activation energies. Below ϳ25 K the noise power is temperature independent suggesting that the kinetics are dominated by tunneling. Our results show that the thermal stability of both the magnetic layers and the quality of the tunnel barrier are important factors in reducing the low-frequency noise in magnetic tunnel junctions.

Equilibrium conductivity fluctuations of mesoscopic domains are found in film and bulk single-crystal manganite colossal magnetoresistive material. Temperature and field dependences of the Boltzmann factors for a collection of two-state fluctuators give measures of the magnetic moment and entropy differences between the states, and of the fluctuator volumes. The large resistance step size implies dramatic current inhomogeneities. Occasional anomalous temperature dependences indicate that the film inhomogeneous phase is stabilized by a repulsive interaction between conducting regions.

Low frequency noise has been measured in magnetic tunnel junctions that have Al 2 O 3 tunnel barriers and magnetoresistance values up to 35% at 295 K. Fluctuations in voltage were found to cross over from Johnson noise to shot noise at low bias voltages, in quantitative agreement with theories of noise in quantum ballistic systems. 1/f resistance noise, where f is frequency, predominates at larger biases and is proportional to the mean current squared. This noise is attributed to trapping processes and it depends sensitively on the relative position of the oxide edge and the ferromagnet-Al interface.

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We study the dynamics of superconducting vortices in Nb rings as the system is continuously driven to the depinning threshold by the slow ramping of an external magnetic field. Miniature Hall probes simultaneously detect local and global flux changes arising from vortex motion. With decreasing temperature, the dynamics evolve continuously from smooth flow to several types of avalanche behavior. In particular, we observe a crossover from broad to narrow size distributions of avalanche events which correspond to global decreases in the flux density gradient rather than local redistributions of flux. We show how this evolution can arise from the magnetothermal instability of the Bean state.