Exact solution of a Langevin equation with nonlinear periodic noise

An exact stochastic average of a Langevin equation with a multiplicative nonlinear periodic noise is performed. The noise is described by an arbitrary periodic function of the diffusion Wiener-Lévy stochastic process. The solution of this stochastic equation is given by periodic solutions of the Hill equation.     

Numerical Integration of a Non-Markovian Langevin Equation with a Thermal Band-Passing Noise

An accurate and fast approach for numerically solving a non-Markovian Langevin equation with a thermal band-passing noise is proposed. The algorithm combines the closed integration for both damping and noise terms with the Runge–Kutta method for nonlinear force in the Markovian Langevin equation transferred from the original equation. The present algorithm is tested through simulating diffusion of a free particle by using different initial distributions, and then a strong superdiffusion is shown. The mean velocity of a particle in a flashing ratchet driven by the band-passing colored noise is calculated numerically. The dependence of the resulting mean velocity on temperature, asymmetry of the ratchet potential, and inertia of the particle is discussed, and some novel behaviors in comparison with the usual model are observed.     

Stability of a nonlinear oscillator with random damping

A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be predicted from the analysis of the moments of the linearized equation. In the case of a white noise, an exact formula for the Lyapunov exponent of the system is derived. We then calculate the critical damping for which the nonlinear system becomes unstable. We also characterize the intermittent structure of the bifurcated state above threshold and address the effect of temporal correlations of the noise by considering an Ornstein-Uhlenbeck noise.     

A method of estimating the noise level in a chaotic time series

An attempt is made in this study to estimate the noise level present in a chaotic time series. This is achieved by employing a linear least-squares method that is based on the correlation integral form obtained by Diks in 1999. The effectiveness of the method is demonstrated using five artificial chaotic time series, the Henon map, the Lorenz equation, the Duffing equation, the Rossler equation and the Chua's circuit whose dynamical characteristics are known a priori. Different levels of noise are added to the artificial chaotic time series and the estimated results indicate good performance of the proposed method. Finally, the proposed method is applied to estimate the noise level present in some real world data sets.     

简谐速度噪声与简谐噪声环境中谐振子的动力学共振

通过求解简谐势场中的广义量子朗之万方程，得到平均能量的精确表达式.由于简谐速度噪声与简谐噪声功率谱的不同特点，两种内部噪声驱动的谐振子在简谐外力的作用下具有不同的共振特征.这些特征可用来检验两种噪声.     

Information entropy of a dynamical system driven by quasimonochromatic noise

This paper shows the Fokker-Planck equation of a dynamical system driven by quasimonochromatic noise. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production for the system is calculated. The relationship between the properties of quasimonochromatic noise and dissipative parameter and their effects on entropy flux and entropy production are discussed.     

Entanglement dynamics in atom-field interaction in the presence of noise: a special application of the Burshtein equation

The entanglement dynamics in a system of the interaction of an atom with a single-mode thermal field in the presence of noise is studied by the Jaynes-Cummings model. Two-state random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained by the Burshtein equation. Although the Burshtein equation is applicable for laser-atom interactions, it is shown that it can be applied to atom-thermal field system as a special case. The solution is used to investigate the entanglement dynamics of the atom-field interaction by calculating a lower bound on concurrence. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity. Moreover, intense noise may generate stronger entanglement compared with the absence of noise.     

Stochastic Resonance in a Linear Fractional Langevin Equation

The fractional Langevin equation is derived from the generalized Langevin equation driven by the additive fractional Gaussian noise. We investigate the stochastic resonance (SR) phenomenon in the underdamped linear fractional Langevin equation under the external periodic force and multiplicative symmetric dichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expressions of the amplitude and signal-to-noise ratio (SNR) of the system. By studying the impacts of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude and SNR. The results indicate that the bona fide SR, conventional SR and the wide sense of SR phenomena occur in the proposed linear fractional system.     

Distribution- and correlation-functions for a laser amplitude

In this paper a contribution to the nonlinear theory of laser noise is given. The lasing field is treated as a classical random variable, the noise is introduced by the concept of fluctuating dipoles. In order to obtain correlation functions the method of distribution functions is employed. The distribution functions are calculated by the Fokker-Planck equation.     

The study on a stochastic system with non-Gaussian noise and Gaussian colored noise

In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker-Planck equation, and the expressions of stationary probability density function and mean first-passage time are presented. Also we explore the effects of correlation between non-Gaussian and Gaussian noise for the mean first-passage time.     

Coherence stabilization of a two-qubit gate by ac fields

We consider a CNOT gate operation under the influence of quantum bit-flip noise and demonstrate that ac fields can change the qubit Hamiltonian in such a way that it approximately commutes with the bath coupling. Then the noise effectively acts as phase noise which improves coherence up to several orders of magnitude while the gate operation time remains unchanged. Within a high-frequency approximation, both purity and fidelity of the gate operation are studied analytically. The numerical treatment with a Bloch-Redfield master equation confirms the analytical results.     

The prediction of jet noise ground effects using an acoustic analogy and a tailored Green's function

An assessment of an acoustic analogy for the mixing noise component of jet noise in the presence of an infinite surface is presented. The reflection of jet noise by the ground changes the distribution of acoustic energy and is characterized by constructive and destructive interference patterns. The equivalent sources are modeled based on the two-point cross-correlation of the turbulent velocity fluctuations and a steady Reynolds-Averaged Navier–Stokes (RANS) solution. Propagation effects, due to reflection by the surface and refraction by the jet shear layer, are taken into account by calculating the vector Green's function of the linearized Euler equations (LEE). The vector Green's function of the LEE is written in relation to that of Lilley's equation; that is, it is approximated with matched asymptotic solutions and Green's function of the convective Helmholtz equation. The Green's function of the convective Helmholtz equation in the presence of an infinite flat plane with impedance is the Weyl–van der Pol equation. Predictions are compared with measurements from an unheated Mach 0.95 jet. Microphones are placed at various heights and distances from the nozzle exit in the peak jet noise direction above an acoustically hard and an asphalt surface. The predictions are shown to accurately capture jet noise ground effects that are characterized by constructive and destructive interference patterns in the mid- and far-field and capture overall trends in the near-field.     

Nonequilibrium Shot Noise Spectrum Through a Quantum Dot in the Kondo Regime:A Master Equation Approach under Self-Consistent Born Approximation

We construct a number(n)-resolved master equation(ME)approach under self-consistent Born approximation(SCBA)for noise spectrum calculation.The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations.We apply this approach to the challenging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum.The proposed n-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach,in the sense of being applicable to the shot noise of transport under small bias voltage,in non-Markovian regime,and with strong Coulomb correlations as favorably demonstrated in the nonequilibrium Kondo system.     

色噪声驱动的双奇异随机系统的熵流与熵产生

讨论一类 (非平衡约束下) 高斯色噪声驱动的双奇异随机系统对应的Fokker-Planck方程，结合Shannon信息熵定义给出此类系统的熵流、熵产生随时间演化的精确表达式.分析(非平衡约束下)所引入的奇异性强度参数、噪声相关时间与耗散参数的相互作用以及对熵流、熵产生的显著影响. 关键词： 信息熵 熵流与熵产生 双奇异随机系统 高斯色噪声     

A method of background noise reduction in lidar data

This paper applies a theoretical approach to the calculation of background noise levels during the analysis of lidar (light detection and ranging) data. We develop a method for the identification of background noise concealed within lidar signals under clear atmospheric or homogeneous aerosol layer conditions and derive an equation for the calculation of these noise levels from a theoretical consideration of the lidar equation. An increasing range-corrected signal indicates that a large amount of background noise exist in the return signal. We calculate the level of background noise by selecting three equidistant points in the return signal from the homogeneous layer and inputting the range and intensity of these points into the derived equation. Background noise calculations using actual lidar signals were in good agreement with calculations based on a simulated lidar signal. The background noise equation was verified using both observational lidar data and a simulated signal, indicating that it provides a reasonable measure of background noise levels in lidar data.     

Testing a theory of aircraft noise annoyance: a structural equation analysis

Previous research has stressed the relevance of nonacoustical factors in the perception of aircraft noise. However, it is largely empirically driven and lacks a sound theoretical basis. In this paper, a theoretical model which explains noise annoyance based on the psychological stress theory is empirically tested. The model is estimated by applying structural equation modeling based on data from residents living in the vicinity of Amsterdam Airport Schiphol in The Netherlands. The model provides a good model fit and indicates that concern about the negative health effects of noise and pollution, perceived disturbance, and perceived control and coping capacity are the most important variables that explain noise annoyance. Furthermore, the model provides evidence for the existence of two reciprocal relationships between (1) perceived disturbance and noise annoyance and (2) perceived control and coping capacity and noise annoyance. Lastly, the model yielded two unexpected results. Firstly, the variables noise sensitivity and fear related to the noise source were unable to explain additional variance in the endogenous variables of the model and were therefore excluded from the model. And secondly, the size of the total effect of noise exposure on noise annoyance was relatively small. The paper concludes with some recommended directions for further research.     

非线性激光场中量子噪声之间的耦合效应

用二维气体激光模型对量子噪声的实部和虚部存在耦合的激光场进行了理论分析，通过福克－普朗克方程导出了定态激光光场强度和位相的分布函数，算出了定态激光强度和位相的平均值，方差和偏斜度，与量子噪声的两个分量为独立随机变量的激光场相比，噪声间的耦合极大地改变了激光场强度和位相的涨落，并引起了激光场强度与位相之间的耦合。