Asymmetric noise probed with a josephson junction

Non-Gaussian Current Fluctuations in a Short Diffusive Conductor

We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the crossover from elastic to inelastic transport.

Asymmetric noise-induced large fluctuations in coupled systems

Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, and epidemiology to engineering and robotics. In the presence of noise and uncertainty, interactions between the individual components can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems, and we show how noise in one part of the system is transmitted through the coupling interface. Working synergistically with the coupling, the noise on one system drives a large fluctuation in the other, even when there is no noise in the second system. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. Uncertainty effects are quantified by showing how characteristic time scales of noise-induced switching scale as a function of the coupling between the two coupled parts of the experiment. In addition, our results show that the probability of switching in the noise-free system scales inversely as the square of reduced noise intensity amplitude, rendering the virtual probability of switching an extremely rare event. Our results showing the interplay between transmitted noise and coupling are also confirmed through simulations, which agree quite well with analytic theory.

Full counting statistics of Andreev tunneling

We employ a single-charge counting technique to measure the full counting statistics of Andreev events in which Cooper pairs are either produced from electrons that are reflected as holes at a superconductor-normal-metal interface or annihilated in the reverse process. The full counting statistics consists of quiet periods with no Andreev processes, interrupted by the tunneling of a single electron that triggers an avalanche of Andreev events giving rise to strongly super-Poissonian distributions.

Improvements to Kramers turnover theory

The Kramers turnover problem, that is, obtaining a uniform expression for the rate of escape of a particle over a barrier for any value of the external friction was solved in the 1980s. Two formulations were given, one by Mel'nikov and Meshkov (MM) [V. I. Mel'nikov and S. V. Meshkov, J. Chem. Phys. 85, 1018 (1986)], which was based on a perturbation expansion for the motion of the particle in the presence of friction. The other, by Pollak, Grabert, and Hänggi (PGH) [E. Pollak, H. Grabert, and P. Hänggi, J. Chem. Phys. 91, 4073 (1989)], valid also for memory friction, was based on a perturbation expansion for the motion along the collective unstable normal mode of the particle. Both theories did not take into account the temperature dependence of the average energy loss to the bath. Increasing the bath temperature will reduce the average energy loss. In this paper, we analyse this effect, using a novel perturbation theory. We find that within the MM approach, the thermal energy gained from the bath diverges, the average energy gain becomes infinite implying an essential failure of the theory. Within the PGH approach increasing the bath temperature reduces the average energy loss but only by a finite small amount of the order of the inverse of the reduced barrier height. Then, this does not seriously affect the theory. Analysis and application for a cubic potential and Ohmic friction are presented.

Singular probability distribution of shot-noise driven systems

We study the stationary probability distribution of a system driven by shot noise. We find that both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For sufficiently low rate of noise pulses they correspond to distribution peaks. We find the positions of the peaks and the corresponding exponents. In the underdamped regime the peak positions are given by a geometric progression. The energy distribution in this case also displays multiple peaks with positions given by a geometric progression. Such structure is a signature of the shot-noise induced fluctuations. The analytical results are in excellent agreement with numerical simulations.

Escape statistics for parameter sweeps through bifurcations

We consider the dynamics of systems undergoing parameter sweeps through bifurcation points in the presence of noise. Of interest here are local codimension-one bifurcations that result in large excursions away from an operating point that is transitioning from stable to unstable during the sweep, since information about these "escape events" can be used for system identification, sensing, and other applications. The analysis is based on stochastic normal forms for the dynamic saddle-node and subcritical pitchfork bifurcations with a time-varying bifurcation parameter and additive noise. The results include formulation and numerical solution for the distribution of escape events in the general case and analytical approximations for delayed bifurcations for which escape occurs well beyond the corresponding quasistatic bifurcation points. These bifurcations result in amplitude jumps encountered during parameter sweeps and are particularly relevant to nano- and microelectromechanical systems, for which noise can play a significant role.

Singular response of bistable systems driven by telegraph noise

We show that weak periodic driving can exponentially strongly change the rate of escape from a potential well of a system driven by telegraph noise. The analysis refers to an overdamped system, where escape requires that the noise amplitude θ exceed a critical value θ(c). For θ close to θ(c), the exponent of the escape rate displays a nonanalytic dependence on the amplitude of an additional low-frequency modulation. This leads to giant nonlinearity of the response of a bistable system to periodic modulation. Also studied is the linear response to periodic modulation far from θ(c). We analyze the scaling of the logarithm of the escape rate with the distance to the saddle-node and pitchfork bifurcation points. The analytical results are in excellent agreement with numerical simulations.

Poisson-noise-induced escape from a metastable state

We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a potential well. The results apply for an arbitrary average rate of noise pulses, from slow pulse rates, where the noise acts on the system as strongly non-Gaussian, to high pulse rates, where the noise acts as effectively Gaussian.

Switching exponent scaling near bifurcation points for non-Gaussian noise

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switching sufficiently close to the bifurcation point, leading to a crossover in the behavior of the switching exponent.