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We explore the profiles of self-polarization effect (SPE) of doped G a A s QD under simultaneous presence of hydrostatic pressure (HP), temperature and in presence of noise. Noise term carries Gaussian white character and it has been administered to the system via two different pathways; additive and multiplicative. Profiles of SPE have been monitored as a function of HP, temperature and noise strength. Under a given condition of HP and temperature, noise marks its prominent signature on the SPE profile. However, the extent to which noise affects the SPE profile visibly depends on the noise strength and the pathway through which noise is introduced. As interesting observations we have found that SPE exhibits minimization at a pressure of ∼ 170 kbar in absence of noise and at ∼ 150 kbar when noise is present. Furthermore, in presence of multiplicative noise SPE exhibits a very faint decrease with increase in T up to T ∼ 420 K. However, beyond T ∼ 420 K, further increase in temperature causes abrupt fall of SPE in a highly sharp way. The findings highlight viable ways of tuning SPE of doped QD system through subtle interplay between HP, temperature and noise.

Charge noise can be detrimental to the operation of quantum dot (QD) based semiconductor qubits. We study the low-frequency charge noise by charge offset drift measurements for Si-MOS devices with intentionally implanted donors near the QDs. We show that the MOS system exhibits non-equilibrium drift characteristics, in the form of transients and discrete jumps, that are not dependent on the properties of the donor implants. The equilibrium charge noise indicates a 1/f noise dependence, and a noise strength as low as $$1\,\mu {\rm{eV}}/\sqrt{{\rm{Hz}}}$$ 1 μ eV / Hz , comparable to that reported in more model GaAs and Si/SiGe systems (which have also not been implanted). We demonstrate that implanted qubits, therefore, can be fabricated without detrimental effects on long-term drift or 1/f noise for devices with less than 50 implanted donors near the qubit.

In this paper, we investigate the stochastic resonance phenomenon in a vegetation ecological system with time delay, at which the vegetation dynamics is assumed to be disturbed by both intrinsic and extrinsic noises. The signal-to-noise ratio is calculated when a weak periodic signal is added to the system. The impacts of time delay τ and correlation strength k between two noises on the signal-to-noise ratio are discussed, respectively. Our research results show that: (i) the increase of τ or k can enhance the stochastic resonance in the signal-to-noise ratio as a function of intrinsic noise strength α ; (ii) on the contrary, the increase of τ or k can weaken the stochastic resonance in the signal-to-noise ratio as a function of extrinsic noise strength D ; and (iii) the increase of τ can lead to double stochastic resonance phenomenon in the signal-to-noise ratio as a function of k .

The auto-correlation function and the cross-correlation function of an autonomous stochastic system with time delays are investigated. We obtain the distribution curves of the auto-correlation function C x ( s ) and C y ( s ) , and the cross-correlation function C x y ( s ) and C y x ( s ) of the stochastic dynamic variables by the stochastic simulation method. The delay time changes prominently the behaviors of the dynamical variables of an autonomous stochastic system, which makes the auto-correlation and the cross-correlation of the autonomous stochastic system alternate oscillate periodically from positive to negative, or from negative to positive, decrease gradually, and finally tends to zero with the decay time. The delay time and the noise strength have important impacts for the auto-correlation and the cross-correlation of the autonomous stochastic delay system. The delay time enhances the auto-correlation and the cross-correlation, on the contrary, the noise strength lowers the auto-correlation and the cross-correlation. Under the time delay, by comparison we further show differences of the auto-correlation and the cross-correlation between the dynamical variables x and y .

We show that a thermally isolated system driven across a quantum phase transition by a noisy control field exhibits anti-Kibble-Zurek behavior, whereby slower driving results in higher excitations. We characterize the density of excitations as a function of the ramping rate and the noise strength. The optimal driving time to minimize excitations is shown to scale as a universal power law of the noise strength. Our findings reveal the limitations of adiabatic protocols such as quantum annealing and demonstrate the universality of the optimal ramping rate., 5 pages, 3 figures, 2 pages of supplemental material

In this work we studied the diffusive behavior of active brownian particles under lateral parabolic confinement. The results showed that we go from subdiffusion to ballistic motion as we vary the angular noise strength and confinement intensity. We argued that the subdiffusion regimes appear as consequence of the restricted space available for diffusion (achieved either through large confinement and/or large noise); we saw that when there are large confinement and noise intensity, a similar configuration to single file diffusion appears; on the other hand, normal and superdiffusive regimes may occur due to low noise (longer persistent motion), either through exploring a wider region around the potential minimum in the transverse direction (low confinement), or by forming independent clusters (high confinement)., 6 pages, 6 figures, accepted for publication in Physica A

The stochastic resonance (SR) for a stochastic bistable system driven by a static force and a periodic square-wave signal as well as by additive white noise is considered from the view of signal-to-noise ratio (SNR). It is found that the SNR appears SR behavior when it is plotted as a function of the additive noise strength or as a function of the system parameters. Moreover, the influence of the static force is opposite to that of the amplitude of the stochastic potential.

This work deals with finite arrays of bistable systems with nearest neighbor coupling. We focus on the statistical equilibrium of a collective variable, as well as its response to a weak time periodic perturbation. By means of numerical simulations we demonstrate the sharp contrast between the system behaviors depending on whether the coupling parameter is positive or negative. The stochastic resonance phenomenon is analyzed in terms of the power spectral amplification and the signal-to-noise ratio of the collective variable. Even though those quantifiers show the typical non-monotonic dependence on the noise strength, they lack, for negative coupling, the large enhancement which has been previously observed for arrays with positive coupling.

Based on the Fokker–Planck description of a single-mode laser system and the projection operator method, the mean relaxation time T of a single-mode laser system with correlations between the real and imaginary parts of the quantum noise as well as the pump noise is studied. It is found that the mean relaxation time T increases with the increasing net gain a0 and decreases with the increasing self-saturation coefficient A. T increases with the increasing pump noise strength Q but decreases with the increasing quantum noise strength D. The mean relaxation time T increases (decreases) with the increasing pump noise self-correlation time τ if a0 > 0 (a0 < 0). T decreases with the increasing |λ| (λ is the coefficient of cross-correlation between the real and imaginary parts of the quantum noise).

Transport of electron pairs in a superconducting junction device in the underdamped case is investigated. It is shown that the capacitance of the junctions can slow the movement of the electron pairs and reduce the net voltage. It is also shown that, for the underdamped case and the overdamped case, the movement of the electron pairs in this superconducting junctions device has some similar features. By controlling the correlation between the additive and multiplicative noise, the flux can be reversed. In addition, if the additive noise strength (or the temperature T) is large enough, a reversal can also be induced.

The forced and overdamped motion of non-interacting particles in a periodic asymmetric potential is studied. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with non-correlated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength. These non-trivial results are explained on the basis of the synchronized motion of the individual particles in the perfect lattice.

We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate., Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figures

The collective motion of the globally coupled maps driven by the external noise is investigated when the number of the maps is finite. A simplest collective motion for the globally coupled maps is found by controlling the noise strength. The dimension of the collective motion exhibits a minimum as a function of the external noise strength when the collective motion is the simplest.

Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the fractal repeller and the critical point of the map. Two methods give a precise meaning to the asymptotic expansion, Borel summation and Shafer approximants. These can then be compared with the escape rate as computed by alternative methods., Comment: 15 pages, 5 postscript figures incorporated into the text; v2: Quadratic Pade (Shafer) method added, also a few references

The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological system is the impulse transmission in neurons and the synchronization of a neural network. Integrating numerically the Fokker-Planck equation we show a self-induced synchronized oscillation. Such an oscillatory state appears in a neural network coupled with a feedback term, when this system is excited by noise and the noise strength is within a certain range., Comment: 12 pages, 18 figures

Triglycine sulfate (TGS) is the first ferroelectric material that has been reported to exhibit the effect of stochastic resonance. We observed the effect experimentally, varying the noise strength added to a periodic signal, that was too weak to cause switching between the two possible states of polarization in ferroelectric TGS. Despite the fact that most of the theoretical predictions could be confirmed in our experiments, there occured some peculiarities that have not been observed in other systems with stochastic resonance. The most obvious effect is the dependence of the spectral amplification and the signal-to-noise-ratio on the direction of noise variation. It can be explained taking into account the mechanism of domain switching in ferroelectric materials.

We study theoretically the dynamics of a system of two magnetizable particles suspended in a non-magnetic fluid subject to a rotating magnetic field when a modulation on the Mason number (ratio of viscous to magnetic forces) is applied. We find, using a periodic modulation, that a resonant-like phenomenon between the periodic modulation of the Mason number and the intrinsic radial oscillation of the system without modulation occurs. For a random perturbation of the Mason number, we obtain an optimum noise strength at which the average interparticle distance reaches the lowest value. When a weak periodic modulation and a noise source are included in the Mason number, stochastic resonance (SR) is found for different frequencies and amplitudes of the modulation. An interpretation of this SR phenomenon is made by means of a threshold crossing mechanism.

We study the two time correlation for the noise driven dynamics of the double-well oscillator in the Suzuki regime. It is seen that for very small noise strength the correaltion function shows a lack of translational invariance for very long times characterised by the Suzuki scaling variable. We see that in this strongly out-of-equilibrium situation, the conventional mode-coupling approximation is not a convenient tool., Comment: 8 pages, no figure

Efficiency of generation of net unidirectional current in an adiabatically driven symmetric periodic potential system is studied. The efficiency shows a maximum, in the case of an inhomogeneous system with spatially varying periodic friction coefficient, as a function of temperature. The ratchet is not most efficient when it gives maximum current. The direction of current may also be reversed as a function of noise strength when, instead, an asymmetric periodic potential is considered., Comment: 14 pages, including 5 figures

Electronic analog experiments on escape over a fluctuating potential barrier are performed for the case when the fluctuations are caused by Ornstein-Uhlenbeck noise (OUN). In its dependence on the relation between the two OUN parameters (the correlation time tau and noise strength Q) the nonmonotonic variation of the mean escape time T as a function of tau can exhibit either a minimum (resonant activation), or a maximum (inhibition of activation), or both these effects. The possible resonant nature of these features is discussed. We claim that T is not a good quantity to describe the resonancelike character of the problem. Independently of the specific relation between the OUN parameters, the resonance manifests itself as a maximal lowering of the potential barrier during the escape event, and it appears for tau of the order of the relaxation time toward the metastable state.

We define magnetization for a 1D bistable map driven by periodic and random forces. Numerical simulations are carried out to investigate the effect of drive amplitude and frequency and noise strength on the area of the hysteresis loop. We observe that for a given amplitude, the profile of the frequency plotted against the corresponding optimal noise for maximum synchronization, D max , can be modeled as an Arrhenius like behaviour.

In this paper we present a hydrodynamic approach to describe the motion of migrating bacteria as a special class of self-propelled systems. Analytical and numerical calculations has been performed to study the behavior of our model in the turbulent-like regime and to show that a phase transition occurs as a function of noise strength. Our results can explain previous experimental observations as well as results of numerical simulations., Comment: 8 pages, 10 figures

Transport of overdamped Brownian particles in deformable potentials is investigated in the presence of asymmetrically unbiased fluctuations. It is found that the deformation of the potential can strongly affect the directed transport. For small noise strength, the current is not always monotonic function of deformable parameter. For large noise strength, there exists a value of deformable parameter at which the current takes its maximum. Therefore, it is possible to obtain the optimal transport by changing the deformation of the potential.

We present a quantitative analysis of grain morphology of self-organizing hexagonal patterns based on the phase-field crystal model to examine the effect of stochastic noise on grain coarsening. We show that the grain size increases with increasing noise strength, resulting in enhanced hexagonal orientation due to noise up to some critical noise level above which the system becomes disordered.

The authors investigate the effects of the synaptic noise in neural networks at finite temperatures. The analytic results are obtained through the use of the path-integral formulation which facilitates performing the quenched average over the random patterns and random noises. We consider the noise effects in the diluted Hopfield model, the fully-connected Hopfield model and the dynamic model, laying emphasis on the interplay with the temperature. In the phase diagrams drawn as functions of the temperature, the storage, and the noise strength, interesting features including re-entrance, first-order transitions as well as second-order transitions are found.

We investigate the effect of noise strength on the macroscopic ordering dynamics of systems with symmetric absorbing states. Using an explicit stochastic microscopic model, we present evidence for a phase transition in the coarsening dynamics, from an Ising-like to a voter-like behavior, as the noise strength is increased past a nontrivial critical value. By mapping to a thermal diffusion process, we argue that the transition arises due to locally-absorbing states being entered more readily in the high-noise regime, which in turn prevents surface tension from driving the ordering process., v2 with improved introduction and figures, to appear in PRL. 4 pages, 4 figures

The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In previous work the coefficients of such an expansion for a one-dimensional map were fitted to a general form containing a few parameters. These parameters were found to be related to the fractal structure of the repeller of the system. The parameter alpha, the "noise dimension", remains to be interpreted. This report presents new data for alpha showing that the relation to the dimensions is more complicated than predicted in earlier work and oscillates as a function of the map parameter, in contrast to other dimension-like quantities., Comment: 7 pages, 5 figures

Waves or pulses propagating along periodic structures cause thermally controlled transport of diffusing defects. The dragging waves/pulses may modulate the amplitude of the substrate as well as the geometry of the boundaries where the defects are confined. The transport efficiency of such a mechanism attains its maximum for an optimal value of the temperature and the modulation speed.

A trapping mechanism is observed and proposed as the origin of the anomalous behavior recently discovered in transport properties of overdamped ratchets subject to external oscillatory drive in the presence of quenched noise. In particular, this mechanism is shown to appear whenever the quenched disorder strength is greater than a threshold value. The minimum disorder strength required for the existence of traps is determined by studying the trap structure in a disorder configuration space. An approximation to the trapping probability density function in a disordered region of finite length included in an otherwise perfect ratchet lattice is obtained. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength due to the presence of the traps., Comment: 21 pages, 6 figures, to appear in PRE

In the present paper, the steady-state properties of a time-delayed cancer growth system that is driven by a correlated multiplicative noise and an additive one are investigated. The numerical results show that the conventional stochastic resonance (SR) phenomenon occurs in the tumor cell growth model for different system parameter values. The results indicate that the additive noise strength always weakens the SR phenomenon, while the time delay mainly increases the SR phenomenon. On the other hand, it is shown that the effects of the strength of the multiplicative noise are different.

We propose and experimentally demonstrate detecting small single-cycle and few-cycle signals by using the symmetric double-well potential of a radio frequency superconducting quantum interference device (rf-SQUID). We show that the response of this bistable system to single- and few-cycle signals has a non-monotonic dependence on the noise strength. The response, measured by the probability of transition from initial potential well to the opposite one, becomes maximum when the noise-induced transition rate between the two stable states of the rf-SQUID is comparable to the signal frequency. Comparison to numerical simulations shows that the phenomenon is a manifestation of stochastic resonance., 5 pages 3 figures

Stochastic resonance (SR) is generally considered as an enhancement of the system response for certain finite values of the noise strength. In particular the signal to noise ratio (SNR) and the signal amplification show a maximum as a function of the noise intensity. This effect has been experimentally observed in many physical systems and also in magnetic systems. However, as far as magnetic systems are concerned, the dynamic features of the systems have been neglected and it has been assumed that the typical relaxation time is negligible. However this is clearly a rough approximation. In order to clarify this relation, in this paper we numerically study magnetic stochastic resonance in several magnetic systems described by dynamic Preisach model.

Triglycine sulfate (TGS) is the first ferroelectric material that has been reported to exhibit the effect of stochastic resonance. We observed the effect experimentally, varying the noise strength added to a periodic signal, that was too weak to cause switching between the two possible states of polarization in ferroelectric TGS. Despite the fact that most of the theoretical predictions could be confirmed in our experiments there occured some peculiarities that have not been observed in other systems with stochastic resonance. The most obvious effect is the dependence of the spectral amplification and the signal‐to‐noise‐ratio on the direction of noise variation. It can be explained taking into account the mechanism of domain switching in ferroelectric materials.

In this paper the vertex weight is introduced into a snowdrift game to study the evolution of cooperative behavior. Compared with the snowdrift game in a traditional square lattice without any weight, cooperation can be promoted under three types of weight distribution: uniform, exponential and power-law distribution. For an intermediate cost-to-benefit ratio (r), in particular, the facilitation effect of cooperation is obvious. Moreover, the influence of undulation amplitude of weight distribution and the noise strength of strategy selection on cooperative behavior are also investigated. They exhibit a nontrivial phenomenon as a function of r. The results are helpful in analyzing and understanding the emergence of collective cooperation that is found widely in many natural and social systems.

We investigate experimentally the scaling of the average time \ensuremath{\tau} between intermittent, noise-induced bursts for a chaotic mechanical system near a crisis. The system studied is a periodically driven (frequency f) magnetoelastic ribbon. Theory predicts that for deterministic crises where \ensuremath{\tau} scales as \ensuremath{\tau}\ensuremath{\sim}\ensuremath{\Vert}f-${\mathit{f}}_{\mathit{c}}$${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ (f${\mathit{f}}_{\mathit{c}}$, f=${\mathit{f}}_{\mathit{c}}$ at crisis), the characteristic time between noise-induced bursts (f\ensuremath{\ge}${\mathit{f}}_{\mathit{c}}$) should scale as \ensuremath{\tau}\ensuremath{\sim}${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$g(\ensuremath{\Vert}f-${\mathit{f}}_{\mathit{c}}$\ensuremath{\Vert}/\ensuremath{\sigma}), where \ensuremath{\sigma} is the noise strength and \ensuremath{\gamma} is the same in both cases. We determine \ensuremath{\gamma} for the low-noise (``deterministic'') system, then add noise and observe that the scaling for \ensuremath{\tau} is as predicted.