Cross-correlated Noises Research Articles

Effect of interference between two colored noises on the stationary states of a Brownian particle.

In this paper we present properties of an external colored cross-correlated noise-driven Brownian system which is coupled to a thermal bath. Multiplicative cross-correlated noises can stabilize the transition state. Thus by monitoring the interference between the noises one can understand the mechanism of a chemical reaction. At the same time, we have investigated how the interference affects the barrier-crossing dynamics. In its presence breakdown of the Arrhenius result occurs. The breakdown becomes prominent if the multiplicative noises become additive in nature. We have also investigated how the power law behavior of the rate constant as a function of damping strength is affected by the properties of external colored noises. Furthermore, we have observed that multiplicative colored cross-correlated noises can induce the resonant activation phenomenon.

Effects of correlation time between noises on the noise enhanced stability phenomenon in an asymmetric bistable system

The effects of the correlation time τ between noises on the noise-enhanced stability (NES) phenomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The expressions for the average escape time from the left metastable state TL and from the right metastable state TR are derived. The results indicate that: i) The NES effect is suppressed as the correlation time τ increases for two metastable states; ii) The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii) In the escape process from the left state, the role of τ is opposite to that in escape from the right state.

Effect of Time Delay and Cross-Correlated Noises on Stochastic Resonance for a Metapopulation System with a Multiplicative Periodic Signal

In this paper, stochastic resonance (SR) in a time-delayed metapopulation system subjected to cross-correlated noises and a multiplicative signal is investigated. By using the fast descent method and the two-state theory, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results show that the conventional SR phenomenon appears in the metapopulation model under different values of the system parameters. The results demonstrate that the strength of the correlation noise λ always plays a decisive role in motivating the SR phenomenon. On the other hand, for the case of λ ＞ 0, the intensities of the multiplicative and additive noises and the time delay can all weaken the effect of SR; for the case of λ ＜ 0, the multiplicative noise can restrain the effect of SR, the weak additive noise can excite the effect of SR, the time delay τ can produce different effects on the SNR under the conditions of different parameters.

Investigating the impact of correlated white noises on the bistability behavior in an optical three-level bistable system

The effect of correlated white noises on the optical bistability behavior of three-level atomic systems is theoretically investigated. Noise-induced bistability is demonstrated in an atomic optical bistable system consisting of three-level atoms in Λ-type configurations confined in an optical ring cavity. The output field as a result of enhanced Kerr nonlinearity induced by atomic coherence in the electromagnetically induced transparency system is variable due to the noises in laser parameters and the cooperativity parameter. Therefore, noise is mainly responsible for such induced bistability in the system. It is found that with the cross-correlation noises, the hysteresis loop of optical bistability can be clearly expanded in comparison with the deterministic case and the atomic system could show multistability behavior. This is specifically considerable for positive cross-correlated noises where it could expand the domain of the hysteresis loop. In the presented atomic system the numerical result shows that noise can induce bistability in the absence of spontaneously generated coherence. Furthermore, it is salient that the noise could induce bistability when the system is below its deterministic threshold for bistability.

Delay and noise induced regime shift and enhanced stability in gene expression dynamics

A quantitative model of autoregulatory gene expression involving a single gene with time delays and cross-correlated noise sources is investigated. The probability density and mean first passage time (MFPT) of the protein concentration are obtained. The impacts of multiplicative (σM) and additive (σA) noise intensities, cross-correlation intensity λ between two noises, time delays τ in the degradation process and θ in the synthesis process and time delay β in both processes on the probability density and MFPT of the regime shifts between high and low protein concentration states are discussed, respectively. These results indicate that (i) the regime shifts from a high (or low) protein concentration state to a low (or high) one can be induced by σM, λ and θ (or σA and β); (ii) the MFPT as a function of the noise intensity σM or σA exhibits one maximum value in the case of λ > 0 or θ > 0, this maximum is a signature of the noise's enhanced stability phenomenon for high protein concentration state; and (iii) τ and β can weaken the stability of high protein concentration state but, in contrast, λ and θ can enhance it in the gene expression dynamics.

Noise and time delay induce critical point in a bistable system

We study relaxation time Tc of time-delayed bistable system driven by two cross-correlated Gaussian white noises that one is multiplicative and the other is additive. By means of numerical calculations, the results indicate that: (i) Combination of noise and time delay can induce two critical points about the relaxation time at some certain noise cross-correlation strength λ under the condition that the multiplicative intensity D equals to the additive noise intensity α. (ii) For each fixed D or α, there are two symmetrical critical points which locates in the regions of positive and negative correlations, respectively. Namely, as λ equals to the critical value λc, Tc is independent of the delay time and the result of Tc versus τ is a horizontal line, but as |λ|>|λc| (or |λ|<|λc|), the relaxation time Tc monotonically increases (or decreases) with the delay time increasing. (iii) In the presence of D = α, the change of λc with D is two symmetrical curves about the axis of λc = 0, and the critical value λc is close to zero for a smaller D, which approaches to +1 or -1 for a greater D.

Effects of cross-correlated noises on the transport of active Brownian particles.

The transport properties of active Brownian particles driven by cross-correlated noises are investigated. Using the Langevin and Fokker-Planck approaches, the theoretical analysis of the model is presented. It is found that correlated noises can produce a net velocity, which stems from the symmetric breaking of the system induced by the correlation between noises. The mean velocity is negative for positive correlation but positive for negative correlation. The mean velocity increases while the effective diffusion decreases as the absolute value of the correlation between the noises increases. Both the mean velocity and the effective diffusion show a nonmonotonic dependence on the multiplicative noise, but a monotonically decreasing dependence on the additive noise.

Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises.

We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equivalent multivariable Ito stochastic differential equation for each possible interpretation of the multivariable Langevin equation. To demonstrate the usefulness and significance of these general results, we consider the motion of Brownian particles. We study in detail the stability conditions for harmonic oscillators with two white noises, one of which is additive, random forcing, and the other, which accounts for fluctuations of either the damping or the spring coefficient, is multiplicative. We analyze the role of cross correlation in terms of the different noise interpretations and confirm the theoretical predictions via numerical simulations. We stress the interest of our results for numerical simulations of stochastic differential equations with an arbitrary interpretation of the stochastic integrals.

Time-delay induced symmetry restoration and noise enhanced stability phenomena under correlated noises in an asymmetric bistable system

We consider the effects of time delay on the probability distribution function and the transition rate in an asymmetric bistable system with cross-correlated noises in this paper. The probability distribution function and the transition rate of the system are calculated analytically and numerically. We find that, by increasing the delay time τ, the symmetry of the asymmetric bistable system is restored and the state transition rate k of the system decreases with the activation rate, which corresponds to the phenomenon of noise enhanced stability.

Stochastic resonance in a two-mode laser system driven by colored cross-correlation noises

Considering a gain-noise model for two-mode laser system driven by a periodic signal and two-color cross-correlation noises, we calculate the power spectrum and signal-to-noise ratio (SNR) of an output signal by means of linear approximation method, and discuss the influence of the system coefficients on SNR. Results show that under a certain condition satisfied by the coefficients of the system and input signals, the stochastic resonance phenomenon may be detected in the evolution of SNR, and also at certain intensities of noise, saturation coefficient c2, cross coupling coefficient b, and input signal frequency Ω.

Facilitated transport and efficiency optimization in a cross-correlated noise ratchet

We study the energetic efficiency of a Brownian particle moving in a spatially symmetric potential with temporally symmetric unbiased fluctuations, which is driven by cross-correlated multiplicative and additive noise. The analytical expressions of the current and efficiency at the quasi-steady state limit are presented. Based on the current and efficiency, it is found that: (i) there exists an optimal value of the temperatures and driving force, at which the current takes its maximum, which means that these parameters can facilitate the transport of Brownian particles; (ii) the efficiency shows a resonant-like phenomenon as a function of the temperatures, the load and the driving force, which implies that these parameters can induce optimized efficiency of energy transformation at finite values; and (iii) the efficiency optimization increases with the increase of the cross-correlation between two noises, i.e. the cross-correlation between two noises can enhance the efficiency optimization.

The sufficient condition for lossless linear transformation for distributed estimation with cross-correlated measurement noises

In most distributed fusion algorithms, the measurement noises in different sensors are often assumed to be uncorrelated, but in practical occasions the assumption may not be met and the measurement noises are often cross-correlated between sensors. So the lossless distributed fusion algorithms with the assumption of uncorrelated measurement noises usually cannot keep their lossless performance in practical applications. Therefore, in the case of cross-correlated measurement noises, the lossless compression rule for distributed estimation is proposed. We prove in theory that the sufficient condition of the lossless compression is the transformation matrix is of full column rank. Using the transformation matrix constructed by the proposed rule, the distributed fusion can achieve the performance of the centralized one. In addition, under this rule two optimal fusion algorithms are proposed and their performances are analyzed.

Optimal sequential and distributed fusion for state estimation in cross-correlated noise

This paper is concerned with the optimal state estimation for linear systems when the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. We derive the optimal linear estimation in a sequential form and for distributed fusion. They are both compared with the optimal batch fusion, suboptimal batch fusion, suboptimal sequential fusion, and the suboptimal distributed fusion where the cross-correlation between the noises are neglected. The comparison is in terms of theoretical filter mean square error and the real root mean square error. Simulation on a target tracking example is given to show the effectiveness of the presented algorithms.

Noise thermometry at ultra low temperatures

We present a contact free cross-correlation noise thermometer experimentally characterized for temperatures between 0.8 K and 45 μK. The noise source is a cold-worked copper cylinder. The fluctuations of magnetic fields due to the thermal motion of the electrons in the copper cylinder are simultaneously monitored by two superconducting quantum interference device magnetometers. A subsequent cross-correlation of both channels reduces the noise contribution of the amplifiers by more than one order of magnitude. This technique covers almost five orders of magnitude in temperature including ultra low temperatures, which were accessible only by platinum nuclear magnetic resonance thermometers so far.

Ultrasensitive force detection with a nanotube mechanical resonator

Since the advent of atomic force microscopy, mechanical resonators have been used to study a wide variety of phenomena, including the dynamics of individual electron spins, persistent currents in normal metal rings and the Casimir force. Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12zNHz(-1/2) at a temperature of 1.2K using a resonator made of a carbon nanotube. An ultrasensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. This detection method also allows us to measure the Brownian vibrations of the nanotube down to cryogenic temperatures. Force sensing with nanotube resonators offers new opportunities for detecting and manipulating individual nuclear spins as well as for magnetometry measurements.

Scattering approach to frequency-dependent current noise in Fabry-Pérot graphene devices

We study finite-frequency quantum noise and photon-assisted electron transport through a wide and ballistic graphene sheet between two metallic leads. The elementary excitations allow us to examine the differences between effects related to Fabry-P\'erot-like interferences and signatures caused by correlations of coherently scattered particles in electron- and holelike parts of the Dirac spectrum. We identify different features in the current-current auto- and cross-correlation spectra and trace them back to the interference patterns of the product of transmission and reflection amplitudes, which define the integrands of the involved correlators. At positive frequencies, the correlator of the autoterminal noise spectrum with final and initial states associated to the measurement terminal is dominant. Phase jumps occur within the interference patterns of corresponding integrands, which also reveal the intrinsic energy scale of the two-terminal graphene setup. The excess noise spectra, as well as the cross-correlation ones, show large fluctuations between positive and negative values. Oscillatory signatures of the cross-correlation noise are due to an alternating behavior of the integrands.

Optimal Fusion Filtering in Multisensor Stochastic Systems with Missing Measurements and Correlated Noises

The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with missing measurements and autocorrelated and cross-correlated noises. The stochastic uncertainties in the measurements coming from each sensor (missing measurements) are described by scalar random variables with arbitrary discrete probability distribution over the interval[0,1]; hence, at each single sensor the information might be partially missed and the different sensors may have different missing probabilities. The noise correlation assumptions considered are (i) the process noise and all the sensor noises are one-step autocorrelated; (ii) different sensor noises are one-step cross-correlated; and (iii) the process noise and each sensor noise are two-step cross-correlated. Under these assumptions and by an innovation approach, recursive algorithms for the optimal linear filter are derived by using the two basic estimation fusion structures; more specifically, both centralized and distributed fusion estimation algorithms are proposed. The accuracy of these estimators is measured by their error covariance matrices, which allow us to compare their performance in a numerical simulation example that illustrates the feasibility of the proposed filtering algorithms and shows a comparison with other existing filters.

The mean extinction time and stability for a metapopulation system driven by colored cross-correlated noises

In this paper, the stability for a metapopulation system driven by colored cross-correlated noises is investigated based on the Levins model. The stationary probability distribution and the explicit expression of the mean extinction time are derived according to the Fokker-Planck equation. Numerical results show that in the case of colored correlation between two noises, the addictive noise and the multiplicative noise intensity weaken the stability of metapopulation, and the correlation strength enhances the stability of metapopulation. If the correlation strength between the two noises is negative, the mean extinction time is a decreasing function of intensities of the two noises, but a increasing function of correlation time; if the correlation strength between the two noises is positive, then the mean extinction time is a decreasing function of addictive noise intensity and correlation time, but a non-monotonic function of multiplicative noise intensity.

The influences of delay time on the stability of a market model with stochastic volatility

The effects of the delay time on the stability of a market model are investigated, by using a modified Heston model with a cubic nonlinearity and cross-correlated noise sources. These results indicate that: (i) There is an optimal delay time τo which maximally enhances the stability of the stock price under strong demand elasticity of stock price, and maximally reduces the stability of the stock price under weak demand elasticity of stock price; (ii) The cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time <τo and the same role for the case of the delay time >τo. Moreover, the probability density function of the escape time of stock price returns, the probability density function of the returns and the correlation function of the returns are compared with other literatures.

Noise thermometry in narrow two-dimensional electron gas heat baths connected to a quasi-one-dimensional interferometer

Thermal voltage noise measurements are performed in order to determine the electron temperature in nanopatterned channels of a GaAs/AlGaAs heterostructure at bath temperatures of 4.2 and 1.4 K. Two narrow two-dimensional (2D) heating channels, close to the transition to the one-dimensional (1D) regime, are connected by a quasi-1D quantum interferometer. Under dc current heating of the electrons in one heating channel, we perform cross-correlated noise measurements locally in the directly heated channel and nonlocally in the other channel, which is indirectly heated by hot electron diffusion across the quasi-1D connection. We observe the same functional dependence of the thermal noise on the heating current. The temperature dependence of the electron energy-loss rate is reduced compared to wider 2D systems. In the quantum interferometer, we show the decoherence due to the diffusion of hot electrons from the heating channel into the quasi-1D system, which causes a thermal gradient.