Trace Formulas for Stochastic Evolution Operators: Weak Noise Perturbation Theory

Periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field-theoretic formalism and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-leading ? corrections to the Gutzwiller trace formula, with long-time averages calculated from periodic orbits of the deterministic system. The perturbative corrections are computed analytically and tested numerically on a simple 1-dimensional system.     

Asymptotics of High Order Noise Corrections

We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.     

Stochastic Resonance in a Bistable System Subject to Dichotomous Noise

The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise (DN) is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-to-noise ratio (SNR) and the spectral power amplification (SPA) have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.     

Stochastic Resonance in a Bistable System Subject to Dichotomous Noise

The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise （DN） is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-tonoise ratio （SNR） and the spectral power amplification （SPA） have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.     

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice, with the nearest- neighbor interaction and quartic anharmonicity. We get the motion equations of our discrete system by adding noise and damping to the set of deterministic motion equations. We define ＂half-time＂ as the time when the amplitude of the envelope soliton decreases by half due to damping. And then the mass, center and half-time of the perturbed envelope soliton are numerically simulated, beginning with the discrete envelope soliton at rest. Results show successfully how noise affects behavior of the envelope soliton.     

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in anFPU-β lattice, with the nearest-neighbor interaction and quartic anharmonicity. We get the motion equations of our discrete system by adding noise and damping to the set of deterministic motion equations. We define ``half-time' as the time when the amplitude of the envelope soliton decreases by half due to damping. And then the mass, center and half-time of the perturbed envelope soliton are numerically simulated, beginning with the discrete envelope soliton at rest. Results show successfully how noise affects behavior of the envelope soliton.     

Test of Trace Formulas for Spectra of Superconducting Microwave Billiards

Experimental tests of various trace formulas, which in general relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart, for spectra of superconducting microwave billiards of varying chaoticity are reviewed by way of examples. For a two-dimensional Bunimovich stadium billiard the application of Gutzwiller's trace formula is shown to yield correctly locations and strengths of the peaks in the Fourier transformed quantum spectrum in terms of the shortest unstable classical periodic orbits. Furthermore, in two-dimensional billiards of the Limaçon family the transition from regular to chaotic dynamics is studied in terms of a recently derived general trace formula by Ullmo, Grinberg and Tomsovic. Finally, some salient features of wave dynamical chaos in a fully chaotic three-dimensional Sinai microwave billiard are discussed. Here the reconstruction of the spectrum is not as straightforward as in the two-dimensional cases and a modified trace formula as suggested by Balian and Duplantier will have eventually to be applied.     

Entropic Stochastic Resonance Driven by Colored Noise

The phenomenon of entropic stochastic resonance （ESR） in a two-dimensional confined system driven by a transverse periodic force is investigated when the colored fluctuation is included in the system. Applying the method of unified colored noise approximation, the approximate Fokker-Planck equation can be derived in the absence of the periodic force. Through the escaping rate of the Brownian particle from one well to the other, the power spectral amplification can be obtained. It is found that increasing the values of the noise correlation time and the signal frequency can suppress the ESR of the system.     

应用随机模型方法预测汽车风噪声

采用随机模型方法,对简化汽车头部外形进行风噪声数值模拟.将计算区域分为声源区域和传播区域,在声源区域采用随机模型构造湍流脉动速度场,传播区域通过求解带源项的线化欧拉方程实现声波向外传播得到声场解.同直接模拟方法相比,该方法具有计算量小、计算所需内存少等优点.数值模拟结果与实验数据吻合较好,验证了该方法预测汽车风噪声的可行性,为研究实际汽车外形的风噪声问题打下基础.     

自催化三分子模型内噪声随机共振

运用化学Langevin方程 ,数值研究了内噪声对单个和单向耦合自催化三分子模型动力学行为的影响 .研究发现 ,对于单个振子体系 ,内噪声可以诱导持续振荡 ,而且随着系统尺度的增大 ,信噪比经过一个极大值 ,从而证明了内噪声随机共振和最佳尺度效应的存在 ;对于单向耦合系统 ,信噪比还随耦合强度的变化而经过极大值 .此外 ,边界条件对耦合体系的内噪声随机共振行为有很大影响 ,非零流条件下 ,耦合可以增强内噪声随机共振 ,而零流条件下 ,耦合会抑制随机共振 ;当耦合强度适宜时 ,每个振子发生随机共振时的尺度几乎相同 ,表明最佳体系尺度和耦合强度有助于体系达到最佳的化学反应状态 .     

Stochastic Resonance Induced by an Asymmetric Two-state Noise

Stochastic resonance （SR） phenomenon of the system that is subject to the asymmetric two-state noise is investigated from the broad sense. It is shown that the amplitudes of the output signal exhibit the non-monotonic dependence on the input signal frequency w, and the parameters describing the asymmetric two-state noise, such as the transition rate A, the order parameter k describing the asymmetric degree of the two-state noise, and the noise strength D.     

Stochastic Resonance Induced by an Asymmetric Two-state Noise

Stochastic resonance (SR) phenomenon of the system that is subject to the asymmetric two-state noise is investigated from the broad sense. It is shown that the amplitudes of the output signal exhibit the non-monotonic dependence on the input signal frequency ω, and the parameters describing the asymmetric two-state noise, such as the transition rate λ, the order parameter k describing the asymmetric degree of the two-state noise, and the noise strength D.     

基于SNGR方法的后缘噪声数值模拟

采用随机噪声产生和传播(SNGR)方法对后缘噪声进行数值模拟.SNGR方法结合随机方法和计算流体力学,耗费较少的计算资源就可以预测噪声水平.数值模拟时采用有限体积法求解雷诺平均Navier-Stokes(RANS)方程;采用有限差分法求解声学扰动方程,数值格式采用色散关系保持(DRP)格式,远场边界条件采用无反射边界条件.以二维平板和NACA0012翼型为例,编制程序,与参考结果对比表明,程序可以预测后缘噪声.     

Static Approach to Renormalization Group Analysis of Stochastic Models with Spatially Quenched Noise

Journal of Statistical Physics - A new “static” renormalization group approach to stochastic models of fluctuating surfaces with spatially quenched noise is proposed in which only...     

两种体系中多重随机共振的噪声调控

通过计算机模拟,介绍一种新的方法来控制两种体系中的多重随机共振,被控参数选为噪声的脉冲间隔或噪声强度。对于对称的二能级的量子耗散体系,调节量子噪声则可以实现对量子多重随机共振的控制。另外还借用不同能级之间跃迁的来解释多重随机共振现象的形成机理。     

Stochastic Resonance in a Harmonic Oscillator with Random Mass Subject to Asymmetric Dichotomous Noise

We examine the stability conditions for the averaged moment of a harmonic oscillator having a quadratic random mass. The joint action of asymmetric dichotomous noise and an additional periodic force leads to stochastic resonance in this linear system, where the amplitude of the output signal shows non-monotonic dependence on the frequency of the input signal and the characteristics of the noise.