色噪声间关联的周期调制对单模激光随机共振的影响

讨论色噪声驱动的单模激光系统在噪声间关联程度受时间周期调制情况下的随机共振.用线性化近似的方法计算了光强功率谱及信噪比.具体讨论色噪声情况下信噪比R受噪声强度D,Q,时间周期调制频率Ω_λ以及噪声自关联时间τ₁,τ₂和噪声间关联程度λ的影响.发现信噪比随噪声强度的变化呈单峰共振,信噪比随时间周期调制频率的变化呈周期性共振,而信噪比随 关键词： 色噪声 时间周期调制 噪声间关联程度 周期性随机共振     

双色噪声驱动光学双稳系统的弛豫时间研究

研究乘性及加性噪声的自关联时间τ₁和τ₂,交叉关联时间τ对光学双稳系统的弛豫时间的影响.弛豫时间T由Mei等所采用的方法得到. 经数值计算, 结果表明: 两噪声间交叉关联时间τ及乘性噪声的自关联时间τ₁延缓系统涨落的消退(T随τ及τ₁的增大而增大);T随加性噪声的自关联时间τ 关键词： 关联噪声 弛豫时间 光学双稳系统     

交叉关联噪声对光学双稳系统平均首通时间的影响

研究了乘性色噪声和加性白噪声驱动的光学双稳系统中噪声对系统两个方向平均首通时间T₊（x_s1→x_s2）和T_-（x_s2→x_s1）的影响（平均首通时间是指从一稳态出发越过势垒到另一稳态所用时间的平均值）.通过Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,利用最速下降法得到T₊（x_s1→x_s2）和T_-（x_s2→x_s1）的表达式.研究发现：乘性噪声强度Q和加性噪声强度D对T₊（x_s1→x_s2）的影响相同,对T_-（x_s2→x_s1）的影响不同;T₊（x_s1→x_s2）随乘性色噪声自关联时间τ的增大而增大,但随噪声间的交叉关联强度λ的增大而减小;T_-（x_s2→x_s1）随τ的增大而减小,随λ的增大而增大. 关键词： 平均首通时间 光学双稳系统 乘性色噪声 加性白噪声     

双色噪声驱动非对称双稳系统平均第一穿越时间研究

利用统一色噪声近似理论,研究乘性色噪声和加性色噪声驱动的非对称双稳系统中,势阱的非对称性和噪声对系统两个方向的平均第一穿越时间T₊（x_s1→x_s2）和T_-（x_s2→x_s1）的影响（x_s1和x_s2是双稳系统的两个稳定点）.数值结果表明：T₊（x_s1→x_s2）随乘性噪声的自关联时间τ₁以及加性噪声的自关联时间τ₂的增大而减小.T_-（x_s2→x_s1）随乘性噪声的自关联时间τ₁以及加性噪声的自关联时间τ₂的增大而增大.在曲线（T₊（x_s1→x_s2）,λ）和（T_-（x_s2→x_s1）,λ）上都存在单峰.T₊（x_s1→x_s2）随非对称系数r的增大而增大,T_-（x_s2→x_s1）随非对称系数r的增大而减小. 关键词： 统一色噪声近似 平均第一穿越时间 加性色噪声 乘性色噪声     

噪声间关联程度的时间周期调制对单模激光随机共振的影响

用线性化近似的方法研究了噪声间关联程度λ受时间周期性调制的单模激光增益模型的光强功率谱及信噪比.具体讨论信噪比R受加法噪声强度D,乘法噪声强度Q及噪声间关联程度λ的影响,以及受周期调制频率Ω_λ,输入信号频率Ω的影响.发现了一些新颖的现象. 关键词： 时间周期调制频率 噪声间关联程度 随机共振 信噪比     

颗粒尺寸分散度对颗粒体系力学和几何结构特性的影响

利用颗粒离散元方法, 研究了由2048个光滑颗粒组成的体系在各向同性压缩条件下, 颗粒尺寸分散度s对颗粒体系力学和几何结构特性的影响. 结果表明: 配位数、剪切模量、静态结构因子以及取向序关联函数等都随分散度的变化而变化, 而力的累积分布不受分散度的影响. 其中, 单分散体系(亦即s=0)的静态结构因子在低波数区域(亦即低k)遵从幂律标度S(k)∝0.2k^-4/3, 各分散度下取向序关联函数峰值符合e指数变化规律g₆(r)∝ae^-r/ξ₆, 其中序关联长度ξ₆随分散度s增大而减小. 关键词： 颗粒物质 尺寸分散度 结构因子 取向序关联     

在相对论性激光-等离子体系统中初始物理参数对激光脉冲的影响

基于相对论性激光-等离子体动力学理论，研究了相对论性激光-等离子体系统中圆偏振入射脉冲激光和等离子体相互作用对激光脉冲宽度的影响. 具体分析了在不同初始物理参数下脉冲激光的脉冲宽度在等离子体传播过程中的变化情况，重点分析了激光脉冲在等离子中压缩. 计算结果表明增加入射激光的强度和入射脉冲宽度以及减小等离子体的初始密度，能够有效地实现脉冲宽度在等离子体中压缩；当激光脉冲的初始参数a₀=0.12和τ=70以及等离子体密度n₀=0.3时，脉冲宽度相对压缩T/τ接近于1/10，从而给出了激光压缩的理论优化参数. 关键词： 相对论性激光-等离子体 激光脉冲宽度 等离子体密度 自压缩     

非线性系统中的关联色噪声

研究了加性噪声和乘性噪声之间的耦合为色噪声时非线性系统的动力学行为.对于不同的噪声关联时间τ,求出了系统的有效本征值λeff和强度相关时间Tc.结果表明,当噪声之间的耦合λ大于零时,关联时间τ的增大可抑制系统在阈值附近的涨落;而当噪声之间的耦合λ小于零时,关联时间τ的增大则加强系统在阈值附近的涨落 关键词： 耦合强度 噪声关联时间 有效本征值 强度相关时间     

实虚部关联的量子噪声和泵噪声对单模激光动力学性质的影响

采用具有实虚部关联的量子噪声和泵噪声驱动的单模激光损失模型，用线性化近似方法研究了反映激光动力学性质的光强关联函数，讨论了光强关联函数随时间的演化；并对线性化近似方法的适用范围进行了详细分析，分别讨论了量子噪声强度、泵噪声强度、量子噪声实虚部关联系数对光强相对涨落的影响，得出在小噪声、远离阈值时，线性化近似方法适用范围扩大；小噪声、远离阈值且当量子噪声实虚部无关联时，线性化近似方法适用范围最大的结论. 关键词： 单模激光 光强关联函数 光强相对涨落     

周期力调制噪声驱动下单模激光系统的多重随机共振

在周期力调制噪声驱动下单模激光系统的光强方程中加入调幅波, 用线性化近似方法计算了系统的光强关联函数和输出信噪比, 并对信噪比进行数值计算和分析, 发现低频调制频率Ω、高频载波频率ω和周期力频率Ω_λ对系统的输出信噪比有很大的影响. 具体表现为信噪比R 随低频调制频率Ω 的变化过程中出现了多重随机共振和极强的单峰共振, 当Ω << ω 时, 系统出现的是多峰共振, 且随着Ω_λ 增加, 共振峰间的距离增大, 峰值位置不变; 当Ω → ω 时, 输出信噪比R迅速增大, 而Ω_λ 的影响被削弱甚至可以忽略, 多峰共振消失; 当Ω = ω 时, 系统出现了极强的单峰共振. 此外, 信噪比随周期力频率的变化呈现振幅减小的多重随机共振, 而随载流频率的变化出现单峰随机共振.     

Study of the normalized intensity correlation function of a single-mode laser system with colored cross-correlated noises

A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time τ and the cross-correlation intensity λ between noises on the normalized intensity correlation function C(s). It is found that if λ＞ 0 (λ＜ 0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time τ, and at large value of τ, the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when λ is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when λ becomes smaller and smaller.     

Moments of the intensity of a single-mode laser driven by coloured pump noises with a cross-correlation between the real and imaginary parts of the quantum noise

By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ_q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity 〈I〉 and variance λ_2 (0) for both below and above the threshold operation, and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ_q makes the 〈I 〉－τ curves exhibit a "re-entrant phase transition". Whether the laser is above or below the threshold, the whole 〈I 〉－τ curve moves down as λ_q increases; however, when λ_q=1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ_2(0)－p′ curve being suppressed (here p′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ_2 (0)－p′ curve as a function of λ_q is similar to that of the 〈I 〉－τ curve against λ_q: that is, whether the laser is above or below the threshold, the λ_2 (0)－p′ curve moves up as λ_q increases; however, when λ_q=1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.τ     

Intensity Correlation Function of a Single-Mode Laser Driven by Two Colored Noises with Colored Cross-Correlation

By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. Moreover, we find that there is a minimum Tmin in the curve of the intensity correlation time versus the pump noise intensity, and the depth and position of Train strongly depend on the quantum noise self-correlation time T2 and cross-correlation time T3.     

Time evolution of the intensity correlation function in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts

Using the linear approximation, we have studied the time evolution of intensity correlation function C（t） in a single-mode laser driven by both the colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts. In the case of the pump noise self-correlation time, we find that the time evolution of C（t） varies with modulation signal frequency Ω, amplitude B, and net gain ɑ0. (i) As the Ω increases, the time evolution of C（t） experiences a process changing from the monotonous descension to the descension with a flat appearing initially, and finally to the a form of damping oscillation; (ii) As the B increases, it experiences from monotonous descension to the appearance of a maximum; (iii) As the net gain ɑ0 increases, it experiences a process repeatedly changing from the monotonous descension to monotonous ascension, and to the appearance of a maximum, finally to monotonous descension again. However, in the case of, the time evolution of C（t） only exhibits a form of damping oscillation .     

Steady-State Analysis of a Single-Mode Laser Driven by Colored Pump Noise with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λq between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Qst(I), the mean (I）, and the variance λ2(0) of the laser intensity. It is shown that cross-correlation intensity λq of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠0), improving the pump parameters monotonously will make the curves of Qst(I) exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λq and τ when the laser is operated near or below threshold. Especially when τ≠0, the heights of the peaks of the curves of λ2(0)-α0 and α3(0)-α0, (here a0 is the net gain coefficient) go up as λq increases. However the entire curves λ2(0)-α0 and λ3(0)-α0 are abruptly suppressed when λq = 1, in similarity to phase transition of stationary intensity distribution.     

Associated relaxation time and the correlation function for a tumor cell growth system subjected to color noises

The associated relaxation time Tc and the normalized correlation function C(s) for a tumor cell growth system subjected to color noises are investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. Based on them, the expressions of Tc and C(s) are derived by means of projection operator method, in which the effects of the memory kernels of the correlation function are taken into account. Performing the numerical computations, it is found: (1) With the cross-correlation intensity |λ|, the additive noise intensity α and the multiplicative noise self-correlation time τ₁ increasing, the tumor cell numbers can be restrained; And the cross-correlation time τ₃, the multiplicative noise intensity D can induce the tumor cell numbers increasing; However, the additive noise self-correlation time τ₂ cannot affect the tumor cell numbers; The relaxation time Tc is a stochastic resonant phenomenon, and the distribution curves exhibit a single-maximum structure with D increasing. (2) The cross-correlation strength λ weakens the related activity between two states of the tumor cell numbers at different time, and enhances the stability of the tumor cell growth system in the steady state; On the contrast, τ₁ and τ₃ enhance the related activity between two states at different time; However, τ₂ has no effect on the related activity between two states at different time.     

Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times

We study a system for a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation. The analytical expression of the stationary intensity distribution (SID) for the laser is derived in the case of three different correlation times. The influences of each stochastic parameter on the SID are discussed, the effects of the noise "colour" and the cross-correlation of noises on the mean intensity , the variance, λ_2(0), and the skewness,λ_3(0) of the single-mode laser are investigated. We find that there are colourful phase transitions for the SID above a threshold, and re-entrant transitions induced by the "colour" of the additive noises. Further research of the curves of -τ_i, λ_2(0)-τ_i, and λ_3(0)-τ_i (i=1,2,3) (where τ_i is the correlation time) shows that the output intensity not only increases with the additive noise correlation time τ_2 and the cross-correlation time τ_3, but also the quality of the output of laser beams is optimized.