Can colored noise improve stochastic resonance?

The phenomenon of stochastic resonance is studied in the presence of colored noise. Several sources of colored noise are introduced and the consequences for the asymptotic time-periodic probability and the (phase-averaged) power spectrum are discussed. Based on space-time symmetry considerations, selection rules for the occurrence of-spikes in the power spectrum are derived. The effect of colored noise on the amplification of small periodic signals is studied in terms of effective, time-periodic Fokker-Planck equations: In overdamped systems driven by colored noise, we find that SR is suppressed with increasing noise color. In contrast, for colored noise induced by inertia (as well as for asymmetric dichotomic noise), one obtains an enhancement of SR. This latter result is obtained by studying the Kramers equation perturbed by a small periodic force.     

Relaxation in establishing a steady-state stochastic process with 1/<Emphasis Type="Italic">f</Emphasis> spectrum and low-frequency spike statistics

According to theory, fluctuations with a power spectrum inversely proportional to frequency (1/f processes) may arise when dissimilar phase transitions simultaneously take place in physical systems with intense white noise. In this work, relaxation effects in establishing a steady-state stochastic process with non-equilibrium phase transitions are described in terms of two nonlinear stochastic differential equations. The results thus obtained carry information on the statistics of large-scale low-frequency spikes. Step “forgetting” of initial conditions is noted. It is numerically shown that the distributions of the durations and maximal values of extreme low-frequency spikes have a power-type form.     

Fluctuations and waves in a spatially distributed system with the 1/<Emphasis Type="Italic">f</Emphasis> spectrum

A spatially distributed system with the 1/ _f spectrum of fluctuation power is modeled by two nonlinear stochastic equations. The numerical methods show the formation of 1/ _f and 1/ _k spectra of extreme fluctuations against the background of the formation and motion of waves under the effect of white noise. The distribution of extreme fluctuations corresponds to the maximum of entropy, which testifies to their stability. Under an external periodic perturbation in the system, it is possible to observe space?time stochastic resonance.     

具有频率噪声的单模激光线性模型随机共振

将频率有涨落的周期信号输入单模激光增益模型,计算出输出光强的相关函数及功率谱,对信噪比随噪声强度和系统参数的变化进行了研究. 结果表明:信噪比随频率噪声强度的变化、抽运噪声强度的变化、量子噪声强度的变化均出现随机共振;信噪比随增益系数和损失系数的变化也出现随机共振. 关键词： 频率噪声 功率谱 随机共振     

On the frequency of oscillations in the pair plasma generated by a strong electric field

We study the frequency of the plasma oscillations of electron–positron pairs created by the vacuum polarization in a uniform electric field with strength E   in the range 0.2Ec<E<10Ec$0.2E_c<E<10E_c$. Following the approach adopted in Ruffini, et al. (2007) [1] we work out one second order ordinary differential equation for a variable related to the velocity from which we can recover the classical plasma oscillation equation when E→0$E\to 0$. Thereby, we focus our attention on its evolution in time studying how this oscillation frequency approaches the plasma frequency. The time-scale needed to approach to the plasma frequency and the power spectrum of these oscillations are computed. The characteristic frequency of the power spectrum is determined uniquely from the initial value of the electric field strength. The effects of plasma degeneracy and pair annihilation are discussed.     

High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link

To significantly improve the frequency references used in radio-astronomy and the precision measurements in atomic physics, we provide frequency dissemination through a 642-km coherent optical fiber link. On the frequency transfer, we obtained a frequency instability of \(3\times 10^{-19}\) at 1,000 s in terms of Allan deviation on a 5-mHz measurement bandwidth, and an accuracy of \(5\times 10^{-19}\) . The ultimate link performance has been evaluated by doubling the link to 1,284 km, demonstrating a new characterization technique based on the double round trip on a single fiber. This method is an alternative to previously demonstrated techniques for link characterization. In particular, the use of a single fiber may be beneficial to long hauls realizations in view of a continental fiber network for frequency and time metrology, as it avoids the doubling of the amplifiers, with a subsequent reduction in costs and maintenance. A detailed analysis of the results is presented, regarding the phase noise, the cycle-slips detection and removal and the instability evaluation. The observed noise power spectrum is seldom found in the literature; hence, the expression of the Allan deviation is theoretically derived and the results confirm the expectations.     

Stochastic resonance in a nonlinear system with a 1/f spectrum

The system of two nonlinear stochastic equations simulating 1/f fluctuations during the interaction of nonequilibrium phase transitions in the presence of an external harmonic force is analyzed using numerical methods. It is shown that the stochastic resonance occurring in the system enhances the output periodic signal under the action of noise. A random process with a 1/f power spectrum corresponds to the Gibbs-Shannon information entropy peak. In stochastic resonance, the information entropy is minimal.     

二维映射神经元模型中频率依赖的随机共振

通过数值模拟方法, 研究了在具有稳定次阈值振荡特性的二维映射神经元体系中, 噪声对体系非线性动力学的调控作用. 通过计算发现了噪声诱导的动作电位和随机共振现象. 另外,还研究了体系的控制参数及输入信号的频率对体系动力学的影响, 发现了该体系中频率依赖的随机共振现象. 关键词： 二维映射神经元模型 次阈值振荡 高斯白噪声 随机共振     

具有固有频率涨落的记忆阻尼线性系统的随机共振

研究了在内噪声、外噪声(固有频率涨落噪声)及周期激励信号共同作用下具有指数型记忆阻尼的广义Langevin方程的共振行为.首先将其转化为等价的三维马尔可夫线性系统,再利用Shapiro-Loginov公式和Laplace变换导出系统响应一阶矩和稳态响应振幅的解析表达式.研究发现,当系统参数满足Routh-Hurwitz稳定条件时,稳态响应振幅随周期激励信号频率、记忆阻尼及外噪声参数的变化存在"真正"随机共振、传统随机共振和广义随机共振,且随机共振随着系统记忆时间的增加而减弱.数值模拟计算结果表明系统响应功率谱与理论结果相符.     

Excess noise peaks in porous silicon-based diode structures

Results of an experimental observation of the voltage oscillations associated with a discrete tunneling of holes in porous silicon at room temperature are presented. The noise characteristics of diode structures with a porous silicon interlayer formed on heavily boron-doped silicon single crystals are studied. Peaks of excessive noise are observed at frequencies of ～1 MHz, at which single-electron oscillations should be expected. The peak noise power is found to increase with current according to the ～2.5 power law and, at a current density of 0.15 A/cm², to exceed the noise power of the receiver by three to four orders of magnitude. The complex shape of the noise spectrum and its extension to the higher frequency region with increasing current are explained by the three-dimensionality of the system of nanometer-sized silicon grains embedded in insulating silicon dioxide of porous silicon.     

de Haas-van Alphen oscillations with non-parabolic dispersions

de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form S(E) ∝ E ^α for a given energy E. The case α = 1 stands for the parabolic energy dispersion. It is demonstrated that the periodicity of the magnetic oscillations in inverse field can depend notably on the temperature. We evaluated analytically the Fourier spectrum of these oscillations to evidence the frequency shift and smearing of the main peak structure as the temperature increases.     

偏置调幅波调制噪声的单模激光随机共振

采用偏置信号的调幅波调制抽运噪声的单模激光增益模型，用线性化近似方法计算了以e指数形式关联的两色噪声驱动下光强的功率谱及信噪比.结果表明，信噪比随着噪声强度的变化、抽运噪声自关联时间的变化、激光系统参数的变化、载波频率及信号频率的变化均存在随机共振现象. 关键词： 抽运噪声 单模激光 随机共振 调幅波     

The energy injection into a fluid by stochastic volume forces and random stirring forces

The wavenumber spectrum of the stationary energy injection rate into an incompressible fluid described by the Navier-Stokes equations is evaluated for some simple realizations of stochastic volume as well as stirring forces. A general relation between energy injection, fluid's response, and force correlations is derived which was previously shown to be particularly simple for Gaussian distributed forces with white noise frequency spectrum. For two kinds of such model volume forces the energy injection rates are calculated: Fluid volume elements of variable size around randomly chosen positions are forced in one model centralsymmetrically in the other one anti-symmetrically under inversion with various force density profiles. The circumstances under which both models display an energy injection rate k ^–1 into a bandd k around the wavenumberk are discussed. As a simple realization of stochastic stirring forces externally moved hard spheres immersed in the fluid are considered. The equation of motion and energy balance for the velocity field of the combined system is discussed. The spectral distribution of energy injection by stirring is shown to be that of a volume force model.     

The so-called 1/Δ f noise

A sinusoidal ac current of frequeencyf _c generates an excess noise in many solidstate conductors. The power spectrum of this noise is calculated starting from the autocorrelation function of the stochastic process. Besides a 1/Δf term the spectrum includes another contribution varying with 1/(f _c+f). In the low frequency range there is white noise.     

The correlation between intrinsic noise and extrinsic noise

The correlation between intrinsic noise and extrinsic noise in a stochastic system is reviewed in this paper. And the contribution of the correlation between intrinsic noise and extrinsic noise to the power spectrum is quantified by simulation through a model in a stochastic system. In addition, the effects of the correlations between intrinsic noise and extrinsic noise to the power spectrum are analyzed clearly. Finally, it is shown that our results can be used to describe the transmission of the noise in modules in more complex stochastic systems.     

Saturated absorption linewidth: Influence of the source frequency noise

The effect of the source FM noise on the lineshape in sub-Doppler saturation spectroscopy is examined both theoretically and experimentally. We show that the line profile is simply given by the convolution of the homogeneous profile with an effective spectrum, depending on the relative values of the sample relaxation time and of the source frequency correlation time but not departing significantly from the source field power spectrum in the usual cases. This result is well supported by a millimeter wave experiment involving a nearly perfect source, frequency modulated by a Gaussian noise.     

Stochastic resonance of a tri-stable system with α stable noise

A tri-stable system excited by weak periodic signal is taken as a model and the stochastic resonance phenomenon is investigated by additive α stable noise in this paper. The laws for the resonance system parameters q, p, skewness parameter r and intensity amplification factor Q of α stable noise to act on the resonant output are explored under different stability indicies α and asymmetric skewness β of α stable noise. The results indicate that a weak signal can be realized by tuning the system parameters q, p and r under the joint action of additive α stable noise, and the interval of q and p which can induce stochastic resonance does not change with α or β. Moreover, a certain rule is found in which adjusting the intensity amplification factor Q of α stable noise can also realize a synergistic effect when studying the noise-induced stochastic resonance, and the interval of Q does not change with α or β; the best value of the characteristic index is $\alpha =1$ under any system parameter, and the best value of the symmetry parameter is $\beta =1$ under any system parameter. So, the system performance is best when $\alpha =1$ and $\beta =1$. The results will contribute to a reasonable selection of parameter-induced stochastic resonance system parameters and noise intensity of noise-induced stochastic resonance under α stable noise.     

Sensitivity of the heterodyne gravitational wave detector

In order to explore the actual astrophysical possibilities of the heterodyne gravitational wave detector we study its main limitation, due to the motion around the Earth and the Sun. This places an intrinsic limit to the time during which the detector stays tuned to the source and prevents us from taking full advantage of the very large quality factor of sources like pulsars. We study the ratio of signal to thermal noise and find, for a wave of given amplitude, that it is proportional to ^4/3 Q ^1/2, where is the frequency of the source andQ the mechanical quality factor. Consideration of possible astrophysical sources shows the difficulty of detection and points to the need for a tunable heterodyne system.     

色关联噪声驱动下双模激光随机共振

运用线性近似方法,计算得到了关联色噪声和输入周期信号作用下双模激光增益模型输出信号光强的功率密度谱和信噪比,讨论了信噪比随系统参数的变化关系.研究结果发现:在系统的参数和输入信号的频率满足一定条件时,信噪比不仅随噪声强度变化出现了传统的随机共振现象,还发现其随自饱和系数c2、输入信号频率°及交叉耦合参数b的变化都出现了随机共振.