1/f noise at a critical nonequilibrium phase transition

The generation of 1/f noise is demonstrated experimentally in a system consisting of a superconducting film carrying a transport current in contact with a boiling liquid coolant. It is found that wide-band 1/f noise with a large amplitude of the fluctuations is observed over a wide range of parameters. This noise is attributed to the fact that the sub-systems in contact have the same character of the relaxational dependences δT(t)∼ t ^−1/2. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 739–742 (10 May 1996)     

Controlling the noise enhanced stability effect via noise recycling in a metastable system

We analyze the role of the delay time τ _d and the fraction ε of recycled noise on the enhancement of the mean first-passage time (MFPT) in a metastable system with recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay. The results indicate that MFPT as a function of the noise intensity D shows either a non-monotonic behavior with a maximum or a divergent behavior, which is the identifying characteristic of the noise enhanced stability (NES) phenomenon. The increasing of τ _d or ε strengthens the NES effect for ε > 0. However, for ε < 0, there is a critical value of τ _d , below which we observe an increase of MFPT whose maximum goes to infinity, and above which the divergent behavior tends to disappear and MFPT versus D shows a transition from one peak to two peaks and eventually one peak as τ _d or |ε| increases. Moreover, we also discuss the effect of different initial conditions. These observations illustrate that the noise recycling may be used as an effective scheme for controlling the NES effect.     

Associated relaxation time and intensity correlation function of a bistable system driven by cross-correlation additive and multiplicative coloured noise sources

The associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method, the analytic expressions of the stationary probability distribution P_st(x), the relaxation time T_c, and the normalized correlation function C(s) of the system are obtained. The effects of the noise intensity, the cross-correlation strength λ and the cross-correlation time τ are discussed. By numerical computation, it is found that the cross-correlation strength |λ| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation time τ delays relaxation of the system from unstable points. The cross-correlation strength λ and the cross-correlation time τ can alter the effects of the pump noise intensity Q. Thus, the relaxation time T_c is a stochastic resonant phenomenon, and distribution curves exhibit a single-maximum structure.     

Performance of YBaCuO thick film rf SQUIDs at 77 K

RF SQUID behaviour has been observed at 77 K in YBaCuO thick films prepared by screen printing technique. A hole shunted with a microbridge type of geometry is patterned manually for observing rf SQUID behaviour. Flux noise spectrum is also studied and it is found to depend on the quality of the film. The spectral density of the flux noise in the white noise region is 1.7×10⁻³ Φ₀/√Hz at 77 K.     

Resonance effects in the nonadiabatic nonlinear quantum dimer

In the presence of 1/f ^β noise, we investigate the logical stochastic resonance (LSR) in an asymmetric bistable model driven by various cycling combinations of two logic inputs. The probability of correct logic outputs is calculated according to true table of logic relationships. Two major results are presented. Firstly, it is shown that the LSR effect can be obtained by changing noise strength. Over entire range of noise variance, white noise can be considered to be better than 1/f noise or 1/f ² noise to obtain clean logic operation. At a smaller noise level, 1/f noise can realize higher output probability than white noise or 1/f ² noise. In the sense, 1/f noise can be considered to be better than white noise or 1/f ². On the other hand, the correct probability can evolves nonmonotonically as noise exponent β increases, and a kind of SR-like effect can be obtained as a result of β. At certain intermediate noise variance, the output probability is able to attain its minimum at β = 1. It is also shown that actually some finite β sometime can be better than β = 0 at small range of noise variance. The study might provide some potential complement to LSR effect in the presence of 1/f ^β noise.     

The underdamped Josephson junction subjected to colored noises

The properties of the underdamped Josephson junction subjected to colored noises were investigated with large and small phase difference (φ). For the case of the large φ, we found numerically that: (i) the probability distribution function of φ exhibits monostability → bistability → monostability transitions as the autocorrelation rate (λ) of a colored noise increases; (ii) in the bistability region the multiplicative noise drives the phase difference to turn over periodically; (iii) the slope K of the linear response of the junction potential difference (〈V 〉) can be somewhat reduced by means of tuning an optimal λ; (iv) the amplitude of φ in response to external sinusoidal signals changes with λ. For the case of small φ, after deriving the analytical expressions of the potential difference amplitude (〈V 〉_max) and the K in the presence of a dichotomous noise, we found nonmonotonic behavior of 〈V 〉_max and the slope K as a function of λ.     

Tuning of tunneling current noise spectra singularities by localized states charging

We report the results of theoretical investigations of tunneling current noise spectra in a wide range of applied bias voltage. Localized states of individual impurity atoms play an important role in tunneling current noise formation. It was found that switching “on” and “off” of Coulomb interaction of conduction electrons with two charged localized states results in power law singularity of low-frequency tunneling current noise spectrum (1/f ^α) and also results on high frequency component of tunneling current spectra (singular peaks appear). The article is published in the original.     

Wavelet Denoising for Tomographically Reconstructed Image

We have developed a wavelet denoising (thresholding) method for a tomographically reconstructed image to which the conventional wavelet methods are not necessarily applicable because of their limitation of applicable noise models. The basic idea of our new method is that noise variance is, in general, spatially varying and the threshold must be adapted to it. Specifically, our algorithm includes two key steps: The first is to estimate local variances in image space to produce a “σ-map”. The second is to calculate the standard deviations of individual wavelet coefficients from the σ-map by a formula of “covariance propagation”. Spatially adaptive thresholds are then given as those proportional to the standard deviations. Our method is applicable to a wider range of noise models, and numerical experiments have shown that it can yield a denoised image with 10% less residual error than that in the boxcar smoothing or the median filtering.     

Noise minimization via deep submicron system-on-chip integration in megapixel CMOS imaging sensors

Infrared sensor designers have long maximized S/N ratio by employing pixel-based amplification in conjunction with supplemental noise suppression. Instead, we suppress photodiode noise using novel SoC implementation with simple three transistor pixel; supporting SoC components include a feedback amplifier having elements distributed amongst the pixel and column buffer, a tapered reset clock waveform, and reset timing generator. The tapered reset method does not swell pixel area, compel processing of the correlated reset and signal values, or require additional memory. Integrated in a 2.1 M pixel imager developed for generating high definition television, random noise is ∼8e-at video rates to 225 MHz. Random noise of ∼30e-would otherwise he predicted for the 5 μm 5 μm pixels having 5.5 fF detector capacitance with negligible image lag. Minimum sensor S/N ratio is 52 dB with 1920 by 1080 progressive readout at 60 Hz, 72 Hz and 90 Hz. Fixed pattern noise is <2 DN via on-chip signal processing. The paper presented there appears in Infrared Photoelectronics, edited by Antoni Rogalski, Eustace L. Dereniak, Fiodor F. Sizov, Proc. SPIE Vol. 5957, 595701 (2005).     

The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ _c =0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ _c , the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ _c , the τ restrains that.     

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/f^α noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.     

Retrieval of the quasi-optimal signal activating the excitable systems using preceding noise samples

We propose a method for obtaining a signal leading to the activation of an excitable dynamic system for a signal energy close to minimal. The efficiency of this technique, which is based on recording and processing of noise samples preceding the activation was tested using the FitzHugh–Nagumo, Hodgkin–Huxley, and Luo–Rudy models as examples. It is shown that the proposed procedure gives good results when the noise intensity is smaller than or close to the system activation energy. The criteria of “low” and “high” intensities of fluctuations are proposed. The method of increasing the stability of the excitable system with respect to “low-intensity” noise by filtering or another way of suppression of the spectral components that make the main contribution to the energetically optimal activation signal is justified. The relation between eigenvalues of the linearized system of the Hamiltonian equations, which describe the optimal trajectories and the activation signal, and eigenvalues of the excitable system linearized near the initial equilibroum state is found.     

Excess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent

The excess 1/f noise in a random lattice with bond resistances r∼exp(−λx), where x is a random variable and λ≪1, is studied theoretically. It is shown that if the correlation function {δr ²}∼r r ^θ+2, then the relative spectral density of the noise in the system is expressed as C _e∼λ^m exp(−λ(1−p _c)), where p _c is the percolation threshold and m=νd (ν is the critical exponent of the correlation length and d is the dimensionality of the problem). It is hypothesized that the exponent m possesses a dual universality: It is independent of 1) the geometry of the lattice and 2) the θ-mechanism responsible for the generation of the local noise. Numerical modeling in a three-dimensional lattice gives m=52.3 for θ=1 and θ=0, in agreement with the hypothesis. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 614–618 (25 April 1996)     

Analysis of the Characteristics of Laser and Superluminescent Diodes

It is shown that superluminescent diodes rank below laser diodes in energy characteristics, but they have a wider emission spectrum and lower noise level. The amplitude-frequency and noise characteristics of the laser diode correlate with each other, whereas there is no such correlation for the superluminescent diode. The photon density distribution along the active area is more homogeneous for the laser diode than for the superluminescent one. Presented at the 5th International Scientific-Technical Conference “Quantum Electronics,” November 22–25, 2004, Minsk, Belarus. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 5, pp. 689–693. September–October, 2005.     

Laboratory spectroscope based on a multichannel radiometer

The parameters of a microwave spectrometer with simultaneous spectrum analysis (i.e., a spectroscope) based on a multichannel radiometer are studied both theoretically and experimentally. It is shown that in the operating mode with a noise sounding signal having a temperature exceeding the receiver noise temperature the limiting sensitivity of the spectroscope to the optical thickness of gas in the cell is restricted by \gg{inmin} ⋍1/Q, where Q is the radiometric gain of the system. The spectroscope sensitivity can be increased by two orders of magnitude in the millimeter wave range by using a receiver with extremely low noise temperature and a strongly cooled radiator. Sensitivity measurements of a 3 mm spectroscope in the OCS line J=7→8 (at frequency ∼97 GHz) give the value ∼ 3·10⁻⁵ cm⁻¹ for a cell of length 1 m and time constant 15 sec, which is comparable with the technical sensitivity limitof scanning spectrometers in the millimeter wave range. The possibilities of improving the spectroscope parameters are discussed. Lobachevsky State University, Nizhny Novgorod; Institute for Physics of Microstructures of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 904–912, July, 1998.     

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.      

Analysis of signal-to-noise enhancement of box-car averagers

The signal-to-noise improvement ratio (SNIR) of a Box-Car averager is calculated for various noise sources such as random white noise, exponentially correlated noise, etc. For a time constant (RC), and a sampling time ε, the quoted value of SNIR as (2RC/ε)^1/2 is shown to be strictly correct only when the noise is white and deviation from this law is expected for other non-white noise sources. The validity of some of the calculated expressions is established by direct measurement of noise output.     

Structure of the attraction zones of the final states in the presence of dynamical period doubling bifurcations

The structure of the attraction zones of the final states associated with dynamical period doubling bifurcations is investigated. It is found that on the “initial value—transition rate” plane the attraction zones of the two possible final states alternate with each other and that a subdivision of the attraction regions occurs with a decrease in the transition rate. It is shown that the boundaries of the attraction zones are smeared out because of the effect of noise and in this situation the fine structure of the attraction zones is destroyed. As analytical and numerical calculations have shown, the critical value of the noise variance, corresponding to the boundary between the dynamical (or predictable) and stochastic (or unpredictable) modes, has a power-law dependence on the transition rate with a typical exponent value of one. The existence of “noise” invariants is also observed: the integrated (over all initial values) probability of achieving the final state is invariant with respect to the noise level. Zh. éksp. Teor. Fiz. 113, 369–380 (January 1998)     

Anomalous transport and relaxation in classical one-dimensional models

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this “conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity κ(L) ∼L^α in the limit of small noise and large system size L. By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite-size and time effects can be effectively controlled. For low noise amplitudes, the α values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario.     

Delayed pulse referencing for cancellation of polychromatic beating noise in grating spectrometry

We use a grating spectrometer with a time resolution of 17.4 μs and a spectral resolution of 5 GHz to analyze a superluminescent source operating near 1350 nm. Polychromatic beating noise is shown to dominate single-shot measurements of the source spectrum; the observed noise level is within 19% of the theoretical beating noise level. By adopting a delayed pulse referencing scheme used previously with wavelength-swept sources, the beating noise is virtually eliminated, allowing spectral measurements limited only by shot noise and camera read noise.