Thermal escape from a metastable state in periodically driven Josephson junctions

Stabilizing effect of volatility in financial markets

In financial markets, greater volatility is usually considered to be synonymous with greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e., the average time a stock return takes to undergo for the first time a large negative (crashes) or positive variation (rallies), as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for 1071 stocks traded in the New York Stock Exchange, we find that this measure of stability displays nonmonotonic behavior, with a maximum, as a function of volatility. Also, we show that the statistical properties of the empirical data can be reproduced by a nonlinear Heston model. This analysis implies that, contrary to conventional wisdom, not only high, but also low volatility values can be associated with higher instability in financial markets. This proposed measure of stability can be extremely useful in risk control.

Resonant activation in piecewise linear asymmetric potentials

This work analyzes numerically the role played by the asymmetry of a piecewise linear potential, in the presence of both a Gaussian white noise and a dichotomous noise, on the resonant activation phenomenon. The features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum, from the initial well to the bottom of the adjacent potential well. Because of the asymmetry of the potential profile together with the random external force uniform in space, we find, for the different asymmetries: (1) an inversion of the curves of the mean first passage time in the resonant region of the correlation time τ of the dichotomous noise, for low thermal noise intensities; (2) a maximum of the mean velocity of the Brownian particle as a function of τ; and (3) an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated. An inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise, behavior confirmed by recent experiments.

Thermal-inertial ratchet effects: negative mobility, resonant activation, noise-enhanced stability, and noise-weakened stability

Transport properties of a Brownian particle in thermal-inertial ratchets subject to an external time-oscillatory drive and a constant bias force are investigated. Since the phenomena of negative mobility, resonant activation and noise-enhance stability were reported before, in the present paper, we report some additional aspects of negative mobility, resonant activation and noise-enhance stability, such as the ingredients for the appearances of these phenomena, multiple resonant activation peaks, current reversals, noise-weakened stability, and so on.

Detection of noise-corrupted sinusoidal signals with Josephson junctions

We investigate the possibility of exploiting the speed and low noise features of Josephson junctions for detecting sinusoidal signals masked by Gaussian noise. We show that the escape time from the static locked state of a Josephson junction is very sensitive to a small periodic signal embedded in the noise, and therefore the analysis of the escape times can be employed to reveal the presence of the sinusoidal component. We propose and characterize two detection strategies: in the first, the initial phase is supposedly unknown (incoherent strategy), while in the second, the signal phase remains unknown but is fixed (coherent strategy). Our proposals are both suboptimal, with the linear filter being the optimal detection strategy, but they present some remarkable features, such as resonant activation, that make detection through Josephson junctions appealing in some special cases.

Noise-induced enhancement of stability in a metastable system with damping

The mean first passage time of a Brownian particle from an initial unstable state in a metastable system with damping is investigated. The system is analyzed in the low to high damping regime, and the role played by the damping parameter is studied. We observe the noise enhanced stability effect for all the initial unstable states under study and for all values of the damping parameter γ investigated. The curves show a behavior of the mean first passage time vs γ very close to that observed for an overdamped particle in the presence of colored noise as a function of the correlation time.

Noise-induced multi-decrease and multi-increase of net voltage in Josephson junctions

In this paper, we investigate the net voltage in the Josephson junction subject to a thermal noise, a dc constant bias electric current and an ac time-periodic electric drive for the overdamped case and underdamped case simultaneously. It is shown that, by increasing the thermal noise strength, the net voltage can be decreased and increased several times as a function of the driving frequency. In addition, noise-enhanced stability is found for the net voltage of the junction.

Experimental study of resonant activation in a noisy bistable vertical-cavity surface-emitting laser with strong periodic excitation

An experimental evidence of the phenomenon of resonance activation (RA) in bistable semiconductor vertical-cavity surface-emitting laser (VCSEL) with a high level of internal noise under strong periodic excitation is presented. It is shown that the mean switching period (MSP) between polarization states passes through a minimum depending on the modulation frequency. From comparing frequency dependencies of the MSP and the coefficient of variation it is demonstrated for different conditions that resonance activation and stochastic resonance (SR) occur at different optimal values of the modulation frequency. The influence of the signal amplitude, the level of noise in VCSEL and asymmetry of bistable quasipotential are also experimentally studied. For large enough modulation amplitudes, RA and SR are accompanied by the phenomenon of the mean switching frequency locking.

Stability measures in metastable states with Gaussian colored noise

We present a study of the escape time from a metastable state of an overdamped Brownian particle in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise-enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau(c) investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noises, depending on the value of tau(c) with respect to the relaxation time of the system.

Resonant activation through effective temperature oscillation in a Josephson tunnel junction

We experimentally investigated the thermal escape from a metastable state in a Josephson tunnel junction subjected to an oscillating effective temperature. A minimum of the average escape time is observed at certain oscillation frequency. Our results confirm that the resonant activation can be caused not only by the oscillating barrier but also by the oscillating temperature. The linear dependence of the minimum average escape time on the resonant frequency suggests that the correlation between the oscillation and the escape process leads to the resonant escape.