Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle

A detailed asymptotic study of the effect of small Gaussian white noise on a relaxation oscillator undergoing a supercritical Hopf bifurcation is presented. The analysis reveals an intricate stochastic bifurcation leading to several kinds of noise-driven mixed-mode oscillations at different levels of amplitude of the noise. In the limit of strong time-scale separation, five different scaling regimes for the noise amplitude are identified. As the noise amplitude is decreased, the dynamics of the system goes from the limit cycle due to self-induced stochastic resonance to the coherence resonance limit cycle, then to bursting relaxation oscillations, followed by rare clusters of several relaxation cycles (spikes), and finally to small-amplitude oscillations (or stable fixed point) with sporadic single spikes. These scenarios are corroborated by numerical simulations.     

单模非线性光学系统的弛豫速率与随机共振

应用变分法研究了一个单模非线性光学系统的弛豫速率对噪声强度的依赖性，并由线性响应理论考察了该系统的随机共振行为.研究结果表明当系统没有偏置时，单稳与多稳情形下的松弛速率对噪声强度的依赖性表现出很大的不同.揭示了对称的一维单稳系统中的随机共振现象，并针对一维单稳系统中随机共振存在的一般条件进行了分析. 关键词： 弛豫速率 随机共振 变分法 线性响应理论     

Effect of microwave-optical double resonance on anomalous Mössbauer spectra

Using Kubo-Anderson stochastic model calculation it is shown that a microwave-optical-Mőssbauer triple resonance (MOMTR) experiment, which is essentially a Mőssbauer resonance study in presence of microwave-optical double resonance (MODR), can measure short relaxation times of the ion's excited state. This is an improvement over the existing MODR technique.     

Pseudospin quantum acoustics in liquids

We call attention to the fact that data on spin-lattice relaxation in liqudis can give information about the rate of resonant acoustic transitions in substances where ordinary electron paramagnetic resonance (epr) and nuclear magnetic resonance (nmr) have been studied. Secondly it is shown that sound coherence may be exploited to discriminate between effects of stochastic Brownian motion and sound exitation. Preliminary experimental data are presented on the sound modulation of the proton spin-echoes in water with magnetic dipoles Cu²⁺.     

Deterministic and stochastic behavior in ferroelectric particles

The response of a ferroelectric particle to an applied harmonic field is studied using the Fokker-Planck equation approach. The size effect in dielectric susceptibility is interpreted as the complementarity between stochastic resonance and response anomaly of the second-order phase transition. The borderline between stochastic and deterministic behavior is established. Two universal volume-independent ratios of the damping rates are predicted and may be verified in the relaxation experiments. The approach can be generalized also to other finite condensed systems.     

Theory of low field resonance and relaxation I

A theory of low field resonance and relaxation is formulated on the basis of the time-convolution equation formalism. A fluctuating field is assumed to be stochastic, and in certain cases, exact solutions are obtained in closed analytic form.Relevance to recent μSR experiments on a random magnetic system is discussed.     

X- and Q-Band Electron Spin Echo Study of Stochastic Molecular Librations of Spin Labels in Lipid Bilayers

Electron spin echo (ESE) of nitroxide spin labels allows detecting fast nanosecond stochastic restricted rotations (stochastic molecular librations), which is a common property of molecules in disordered media including biological systems. Under the typical experimental conditions, the anisotropic electron paramagnetic resonance (EPR) spectrum of a nitroxide is only partly excited by microwave pulses, which allows selecting an anisotropic contribution to the transverse spin relaxation by comparing echo decays at different spectral positions. On the other hand, for low-amplitude orientational motion, the excitation bandwidth is large enough to cover the range of spectral diffusion occurring during the echo formation. To verify that the two-pulse echo decay is indeed related to fast motions, the stimulated electron spin echo can be used. In addition, theory predicts an increase of the relaxation rates at higher microwave resonance frequency. To check this prediction, in the present work we performed a comparative study of ESE decays at microwave X- and Q-bands, for spin-labeled lipids in the gel phase of a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer. A good agreement found between experimental data and computer simulation provides additional justification for the model of fast stochastic molecular librations.     

Oscillation regularity in noise-driven excitable systems with multi-time-scale adaptation

We investigate oscillation regularity of a noise-driven system modeled with a slow after-hyperpolarizing adaptation current (AHP) composed of multiple-exponential relaxation time scales. Sufficiently separated slow and fast AHP time scales (biphasic decay) cause a peak in oscillation irregularity for intermediate input currents I, with relatively regular oscillations for small and large currents. An analytic formulation of the system as a stochastic escape problem establishes that the phenomena is distinct from standard forms of coherence resonance. Our results explain data on the oscillation regularity of the pre-B?tzinger complex, a neural oscillator responsible for inspiratory breathing rhythm generation in mammals.     

Effect of anomalously slow motions of particles with spins of 1/2 on the shape of the magnetic resonance line of pairs of particles

A non-Markovian version of the Liouville stochastic equation was used to analyze spin relaxation in a pair of particles with spins 1/2 and the dipole-dipole interaction between the spins. The particles were involved in anomalously slow stochastic relative rotation described by the angular correlation function K(t) ～ 1/t ^α with α < 1. The Liouville stochastic equation could be used to describe memory effects in the kinetic dependence of rotational relaxation resulting in a very slow descent of K(t). Our analysis showed that the anomalous relative motion of radicals manifested itself in special features of the shape of the magnetic resonance line of the particle pair.     

Relaxation at critical points: Deterministic and stochastic theory

A generalized critical point can be characterized by non-linear dynamics. We formulate the deterministic and stochastic theory of relaxation at such a point. Canonical problems are used to motivate the general solutions. In the deterministic theory, we show that at the critical point certain modes have polynomial (rather than exponential) growth or decay. The stochastic relaxation rates can be calculated in terms of various incomplete special functions. Three examples are considered. First, a substrate inhibited reaction (marginal type dynamical system) is treated. Second, the relaxation of a mean field ferromagnet is considered. We obtain a result that generalizes the work of Griffiths et al. Third, we study the relaxation of a critical harmonic oscillator.     

Stochastic resonance in single-domain nanoparticles with cubic anisotropy

The signal-to-noise ratio for magnetic stochastic resonance in a superparamagnetic particle with cubic anisotropy is shown to be strongly dependent on the Larmor precession damping α. This phenomenon is due to the coupling of the relaxation and precession modes and can be used for measuring α. The dependence of the signal-to-noise ratio on α is characteristic of particles with nonaxial anisotropy; so the effect is absent in uniaxial particles.     

一种单稳随机共振系统信噪比增益的数值研究

采用四阶Runge-Kutta数值求解方法, 发现一种单稳随机共振系统信噪比增益的随机共振现象, 并且在一定的条件下系统信噪比增益大于1.通过调节单稳随机共振系统参数可以改变信噪比增益.本文结果拓展了这类单稳的已有研究范围, 在信号检测与处理以及通信领域有着潜在的应用价值. 关键词： 单稳随机共振 信噪比增益 数值分析 非线性     

Master equations for time correlation functions of a quantum system interacting with stochastic perturbations and applications to emission and absorption line shapes

The stochastic and quantum dynamics of open quantum systems interacting with stochastic perturbations in considered. The master equations for one time and multi-time correlation functions of such a system are derived to all orders in the interaction with the stochastic perturbations. The importance of the non-markovian character of such equations in the study of various problems in optical resonance is discussed. The simplified form of the non-markovian master equations in Born approximation is also given. It is shown that such non-markovian master equations in Born approximation are exact if there is only one random perturbation, of the telegraphic signal type, acting on the system. The master equations for the linear response functions of an open system interacting with stochastic perturbations are also derived. The non-markovian master equations for multitime correlations are used to study the behaviour of two level atoms interacting with fluctuating laser fields. Both amplitude and phase fluctuations are taken into account. Explicit results are presented for the spectrum of resonance fluorescence, absorption spectrum, photon antibunching effects etc. The calculations are done for arbitrary values of the relaxation parameters and intial conditions. In general the fluorescence spectrum is found to be asymmetric for off resonant fields.     

Magnetic Resonance of Impurity Spin in Slow Fluctuating Local Field

A basic model of magnetic resonance is considered. The model takes into account external static and orthogonal to it rotating magnetic fields together with fluctuating (local) field directed along the static field. The local field is considered as smooth normal stochastic process. New solutions for longitudinal relaxation are obtained in the region of adiabatic slow fluctuations and nonadiabatic losses are estimated.     

Exact solutions to chaotic and stochastic systems

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems. (c) 2001 American Institute of Physics.     

Additive noise in noise-induced nonequilibrium transitions

We study different nonlinear systems which possess noise-induced nonequlibrium transitions and shed light on the role of additive noise in these effects. We find that the influence of additive noise can be very nontrivial: it can induce first- and second-order phase transitions, can change properties of on-off intermittency, or stabilize oscillations. For the Swift-Hohenberg coupling, that is a paradigm in the study of pattern formation, we show that additive noise can cause the formation of ordered spatial patterns in distributed systems. We show also the effect of doubly stochastic resonance, which differs from stochastic resonance, because the influence of noise is twofold: multiplicative noise and coupling induce a bistability of a system, and additive noise changes a response of this noise-induced structure to the periodic driving. Despite the close similarity, we point out several important distinctions between conventional stochastic resonance and doubly stochastic resonance. Finally, we discuss open questions and possible experimental implementations. (c) 2001 American Institute of Physics.     

Stochastic resonance and chaotic resonance in bimodal maps: A case study

We present the results of an extensive numerical study on the phenomenon of stochastic resonance in a bimodal cubic map. Both Gaussian random noise as well as deterministic chaos are used as input to drive the system between the basins. Our main result is that when two identical systems capable of stochastic resonance are coupled, the SNR of either system is enhanced at an optimum coupling strength. Our results may be relevant for the study of stochastic resonance in biological systems.     

Fourier-transform EPR at high-field/high-frequency (3.4 T/95 GHz) using broadband stochastic microwave excitation

Stochastic excitation with a full-width-half-maximum bandwidth of 250 MHz was used to perform Fourier-transform (FT) high-field/high-frequency electron paramagnetic resonance (EPR) at 3.4T/95 GHz (W-band). Thereby, the required microwave peak power is reduced by a factor of tau(p)/T1 as compared to equivalent pulsed FT EPR in which the spin system with spin-lattice relaxation time T1 is excited by a single microwave pulse of length tau(p). Stochastic EPR is particularly interesting under high-field/high-frequency conditions, because the limited output power of mm microwave sources, amplifiers, and mixers makes pulse FT EPR in that frequency domain impossible, at least for the near future. On the other hand, FT spectroscopy offers several advantages compared to field-swept magnetic resonance methods, as is demonstrated by its success in NMR and X-band EPR. In this paper we describe a novel stochastic W-band microwave bridge including a bimodal induction mode transmission resonator that serves for decoupling the microwave excitation and signal detection. We report first EPR measurements and discuss experimental difficulties as well as achieved sensitivity. Moreover, we discuss future improvements and the possibility for an application of stochastic W-band FT EPR to transient signals such as those of photoexcited radical pairs in photosynthetic reaction centers.     

岩板顺层斜坡和直坡演化过程中的随机共振及混沌

对岩板顺层倾斜边坡和直立边坡变形弯曲的演化过程进行了研究.发现岩板顺层斜坡和直坡在其演化过程中有随机共振和混沌现象.当随机共振发生时，即使较小的随机因素也可引起坡体较大的变形弯曲.随机混沌是由于环境因素的周期性变化，特别是每天和每年的周期性变化所致，混沌的出现使得对滑坡的预测和预报变得较为困难. 关键词：