Abstract:
We present here a short review of mainly experimental properties of noise as disordered systems are driven into non-ohmic regimes by applying voltages of few volts only. It is found that the noise does not simply follow the resistance in that the direction of change of noise could be opposite to that of resistance. It is discussed how this and other properties make the noise a complementary and incisive tool for studying complex systems, particularly its dynamic properties. Study of noise in non-ohmic regimes in physical systems is rather in a nascent stage. Some of the open issues are highlighted.

Abstract:
Out-of-equilibrium disordered systems may form memories of external driving in a remarkable fashion. The system "remembers" multiple values from a series of training inputs yet "forgets" nearly all of them at long times despite the inputs being continually repeated. Here, learning and forgetting are inseparable aspects of a single process. The memory loss may be prevented by the addition of noise. We identify a class of systems with this behavior, giving as an example a model of non-brownian suspensions under cyclic shear.

Abstract:
We propose that memory effects in the conductivity of metallic systems can be produced by the same two levels systems that are responsible for the 1/f noise. Memory effects are extremely long-lived responses of the conductivity to changes in external parameters such as density or magnetic field. Using the quantum transport theory, we derive a universal relationship between the memory effect and the 1/f noise. Finally, we propose a magnetic memory effect, where the magneto-resistance is sensitive to the history of the applied magnetic field.

Abstract:
We report the investigation of conductance fluctuation and shot noise in disordered graphene systems with two kinds of disorder, Anderson type impurities and random dopants. To avoid the brute-force calculation which is time consuming and impractical at low doping concentration, we develop an expansion method based on the coherent potential approximation (CPA) to calculate the average of four Green's functions and the results are obtained by truncating the expansion up to 6th order in terms of "single-site-T-matrix". Since our expansion is with respect to "single-site-T-matrix" instead of disorder strength $W$, good result can be obtained at 6th order for finite $W$. We benchmark our results against brute-force method on disordered graphene systems as well as the two dimensional square lattice model systems for both Anderson disorder and the random doping. The results show that in the regime where the disorder strength $W$ is small or the doping concentration is low, our results agree well with the results obtained from the brute-force method. Specifically, for the graphene system with Anderson impurities, our results for conductance fluctuation show good agreement for $W$ up to $0.4t$, where $t$ is the hopping energy. While for average shot noise, the results are good for $W$ up to $0.2t$. When the graphene system is doped with low concentration 1%, the conductance fluctuation and shot noise agrees with brute-force results for large $W$ which is comparable to the hopping energy $t$. At large doping concentration 10%, good agreement can be reached for conductance fluctuation and shot noise for $W$ up to $0.4t$. We have also tested our formalism on square lattice with similar results. Our formalism can be easily combined with linear muffin-tin orbital first-principles transport calculations for light doping nano-scaled systems, making prediction on variability of nano-devices.

Abstract:
For a long time, it has been known that the power spectrum of Barkhausen noise had a power-law decay at high frequencies. Up to now, the theoretical predictions for this decay have been incorrect, or have only applied to a small set of models. In this paper, we describe a careful derivation of the power spectrum exponent in avalanche models, and in particular, in variations of the zero-temperature random-field Ising model. We find that the naive exponent, (3-tau)/(sigma nu z), which has been derived in several other papers, is in general incorrect for small tau, when large avalanches are common. (tau is the exponent describing the distribution of avalanche sizes, and (sigma nu z) is the exponent describing the relationship between avalanche size and avalanche duration.) We find that for a large class of avalanche models, including several models of Barkhausen noise, the correct exponent for tau<2 is 1/(sigma nu z). We explicitly derive the mean-field exponent of 2. In the process, we calculate the average avalanche shape for avalanches of fixed duration and scaling forms for a number of physical properties.

Abstract:
We present results of conductance-noise experiments on disordered films of crystalline indium oxide with lateral dimensions 2microns to 1mm. The power-spectrum of the noise has the usual 1/f form, and its magnitude increases with inverse sample-volume down to sample size of 2microns, a behavior consistent with un-correlated fluctuators. A colored second spectrum is only occasionally encountered (in samples smaller than 40microns), and the lack of systematic dependence of non-Gaussianity on sample parameters persisted down to the smallest samples studied (2microns). Moreover, it turns out that the degree of non-Gaussianity exhibits a non-trivial dependence on the bias V used in the measurements; it initially increases with V then, when the bias is deeper into the non-linear transport regime it decreases with V. We describe a model that reproduces the main observed features and argue that such a behavior arises from a non-linear effect inherent to electronic transport in a hopping system and should be observed whether or not the system is glassy.

Abstract:
We report results of large-scale Monte Carlo simulations of superfluid--insulator transitions in commensurate 2D bosonic systems. In the case of off-diagonal disorder (quantum percolation), we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is $z=1.65 \pm 0.2$. In the case of diagonal disorder, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in the crossover to the generic universality class (apparently with $z=2$). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid--Mott-insulator transition.

Abstract:
We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where a single domain wall slips through a series of positions when the external field is increased, and (b) large disorder regime, which is characterized with nucleation of many domains. The effects of finite concentration of nonmagnetic ions and variable driving rate on the scaling exponents is discussed in both regimes. The universal scaling behavior at low disorder is shown to belong to a class of critical dynamic systems, which are described by a fixed point of the stochastic transport equation with self-consistent disorder correlations.

Abstract:
We present a novel method to compute the phase space distribution in the nonequilibrium stationary state of a wide class of mean-field systems involving rotators subject to quenched disordered external drive and dissipation. The method involves a series expansion of the stationary distribution in inverse of the damping coefficient; the expansion coefficients satisfy recursion relations whose solution requires computing a sparse matrix, making numerical evaluation simple and efficient. We illustrate our method for the paradigmatic Kuramoto model of spontaneous collective synchronization and for its two mode generalization, in presence of noise and inertia, and demonstrate an excellent agreement between simulations and theory for the phase space distribution.

Abstract:
We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the occupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find evidence for a dynamical phase transition well below the transition temperature of the pure system.