Photon-added coherent states for the Morse oscillator

In the paper we have constructed and investigated some properties of the Perelomov's “generalized coherent states” and photon-added coherent states for the Morse one-dimensional Hamiltonian (MO-PACSs), using the SU(2) group generators. We have found the integration measure in the resolution of unity and we have calculated some expectation values in the MO-PACSs representation. Using these states, the diagonal P-representation of the density operator is constructed as a new result for Morse potential. In addition, we have calculated some thermal expectation values for the quantum canonical diatomic gas of the Morse oscillators.     

On the Morse oscillator with a kinetic coupling

We show that a linear change of variables proves simpler to treat kinetic couplings in one-dimensional two-particle systems than a recently proposed representation based on the eigenvectors of the relative position and total momentum [H. Fan et al., Phys. Lett. A 213 (1996) 226]. As a particular example we consider the Morse oscilltor recently treated by the latter method.     

Classical treatment of vibration-rotation intensities for the Morse oscillator

The effect of vibration-rotation interaction on spectral line intensities is treated classically for the Morse oscillator. To describe the distribution of intensity in the R and P branches, one must take into account both the vibrational (radial) and the rotational (perpendicular) dipole moment functions. When this is done, the leading terms for the Fourier coefficients of these functions, as well as the Herman-Wallis factors, agree exactly with the corresponding quantum mechanical matrix elements in the Dunham limit.     

Excitation of the Morse oscillator by an ultrashort chirped pulse

The excitation of the classic Morse oscillator by an ultrashort electromagnetic pulse with a linear frequency chirp is studied theoretically. Formulas are derived for the oscillation amplitude and the radiation power averaged over a period as functions of the excitation energy for free oscillations of the Morse oscillator. Analytical expressions for describing the oscillator motion after the end of the pulse are obtained in the harmonic limit. In the general case of arbitrary parameters of the problem, the specific features of an excited Morse oscillator are analyzed numerically. Prominence is given to the effect of chirp on the excitation energy. The consideration is performed in terms of dimensionless variables, which makes it possible to apply the results obtained to a wide range of molecular systems and exciting-pulse parameters.     

Vibrational resonance in feedforward network

This paper investigates vibrational resonance in multi-layer feedforward network (FFN) based on FitzHugh-Nagumo (FHN) neuron model. High-frequency stimuli can improve the input-output linearity of firing rates, especially for the inputs with low firing rate. For FFN network, it is found that high-frequency disturbances play important roles in enhancing the propagation of weak signal through layers. Synfire-enhanced phenomenon of signal propagation is also observed in multi-layers network, when the signal transmission is affected by high-frequency disturbances. Network connections are found to be important for the propagation of weak signal. Besides that, the characteristics of high-frequency stimuli such as heterogeneity and frequency can also modulate the propagation of neural code through layers.     

Conventionalvs. Gauge-invariant quantum transition probabilities in simple systems. Morse oscillator

Summary Gauge-invariant transition and survival probabilities for a Morse oscillator initially prepared in its ground state are evaluated for the case of intense and short-duration pulses by a nonperturbative approach founded on the solution of the dynamical problem in terms of a Magnus formalism. False probabilities built up from ?conventional”,i.e. gaugedependent, amplitudes are also obtained and contrasted to the true transition probabilities as a test for the difference between them.

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Riassunto Il problema della gauge-invarianza delle probabilità di transizione calcolate in condizioni generali, che è stato riconsiderato da vari autori anche in anni recenti, si esamina dal punto di vista applicativo per il caso di un oscillatore di Morse sottoposto all’azione di un intenso impulso di radiazione di breve durata. Probabilità gauge-invarianti e (false) probabilità, ottenute da ampiezze ?convenzionali?, sono confrontate e discusse.

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Резюме Проблема калибровочной инвариантности вероятности перехода, вычисленной в общем случае, которая рассматривалась рядом авторов, исследуется применительно к осциллятору Морса, взаимодействующему с интенсивным импульсом излучения малой длительности. Сравниваются и обсуждаются калибровочно-инвариантные вероятности и (ошибочные) вероятности, полученные с помощью ?обычных?, т.е. зависящих от калибровки, амплитуд.

     

Vibrational resonance in excitable neuronal systems

In this paper, we investigate the effect of a high-frequency driving on the dynamical response of excitable neuronal systems to a subthreshold low-frequency signal by numerical simulation. We demonstrate the occurrence of vibrational resonance in spatially extended neuronal networks. Different network topologies from single small-world networks to modular networks of small-world subnetworks are considered. It is shown that an optimal amplitude of high-frequency driving enhances the response of neuron populations to a low-frequency signal. This effect of vibrational resonance of neuronal systems depends extensively on the network structure and parameters, such as the coupling strength between neurons, network size, and rewiring probability of single small-world networks, as well as the number of links between different subnetworks and the number of subnetworks in the modular networks. All these parameters play a key role in determining the ability of the network to enhance the outreach of the localized subthreshold low-frequency signal. Considering that two-frequency signals are ubiquity in brain dynamics, we expect the presented results could have important implications for the weak signal detection and information propagation across neuronal systems.     

Perturbed Morse oscillator calculations of vibrational effects on quadrupole coupling in alkali halides

Formulas are obtained for the variation of the quadrupole coupling constant with vibrational state of an ionic diatomic molecule, using the pertubed Morse oscillator formalism. Results are apllied to NaF, KF, RbF, CsF and KCI, and compared with measured values. Systematic discrepancies are noted, which for the alkali fluorides increase with the atomic number of the alkali metal. Possible explanations include a variation of ionicity with vibrational states and a departure from 1/r³ dependencies of the electric field gradient. Calculations of dependencies of eQq on molecular rotation are also presented.     

二维格子神经元网络的振动共振和非线性振动共振

本文采用数值模拟的方法, 在通过电突触耦合或化学突触耦合的二维格子神经元网络中, 研究了FitzHugh-Nagumo神经元受到双频信号输入时神经元网络对低频信号的响应特性. 结果表明:当固定受到双频输入信号的神经元在体系中所占的比例且FitzHugh-Nagumo神经元参数处于可激发区域时双频信号中的高频部分可诱导出动作电位产生, 而且随着高频输入信号强度的增加, 神经元网络对低频输入信号响应先增大后减小, 出现了极大值, 即发生了振动共振现象. 另外本文还研究了神经元网络对低频输入信号的二次谐波的响应, 同样发现了非线性振动共振现象, 并且体系对低频信号的响应随着其频率ω 的增加也产生共振现象, 即发生了双共振现象. 上述共振现象在以电突触耦合的二维格子神经元网络中和以化学突触耦合的二维格子神经元网络中都可以观察到. 当固定双频输入信号中高频输入信号强度时, 随着受到双频输入信号的神经元在体系中所占比例的变化, 电突触耦合的二维格子神经元网络对低频输入信号的响应与化学突触耦合的二维格子神经元网络对低频输入信号的响应相比有很大的不同.     

Vibrational resonance in fractional-order overdamped multistable systems

We investigated the vibrational resonance in fractional-order overdamped multistable systems theoretically and numerically. For a given fractional order p, our results show that the response amplitude exhibits a series of peaks as the frequency or the amplitude of the high frequency input varies. However, when the low-frequency input increases, the response amplitude exhibits unimodal resonance for 1?<?p?<?2. Additionally, for different values of p, whether the response amplitude changes monotonically depends on the degree of spatial potential asymmetry. The mechanism by which p affects the resonance behavior is analyzed. Our results indicate that the value of p affects the resonance behavior by either altering the conditions under which the response amplitude attains its extreme values, or by altering the oscillating frequency of the response amplitude with varying systematic parameters.     

Stochastic resonance in an over-damped linear oscillator

For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function,we study the stochastic resonance(SR) in this paper. Using the Shapiro–Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio(SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.     

V2-dependence of centrifugal constants of H2O molecules in the Morse oscillator model

It is shown in this paper that the centrifugal constantsC ^l (t) calculated in the Morse, oscillator model for the sequence from the operator H _red ^(t) , which is used in processing the rotational levels of the H₂O molecule, are linked by recurrence relations, which enables H _z ^(t) –H _z ^(O) to be given in closed form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 56–58, October, 1982.     

过阻尼谐振子的随机共振

研究了由交叉相关高斯白噪声驱动的过阻尼谐振子的随机共振,其中加法噪声被周期信号所调制,运用平稳关联函数的傅里叶变换,导出了过阻尼谐振子随机模型信噪比的精确表达式.结果揭示:在过阻尼谐振子的随机模型中存在二类随机共振.一类随机共振表现为信噪比随乘法噪声强度Q变化的曲线存在共振峰,另一类随机共振表现为信噪比随振子频率ω变化的曲线存在共振峰.大幅度改变信号频率Ω值的大小,信噪比随乘法噪声强度Q变化的曲线有单峰,一峰一谷和单调变化三种不同的形式.     

Vibrational resonance in Duffing systems with fractional-order damping

The phenomenon of vibrational resonance (VR) is investigated in over- and under-damped Duffing systems with fractional-order damping. It is found that the factional-order damping can induce change in the number of the steady stable states and then lead to single- or double-resonance behavior. Compared with vibrational resonance in the ordinary systems, the following new results are found in the fractional-order systems. (1) In the overdamped system with double-well potential and ordinary damping, there is only one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for these new resonance behaviors is the value of the fractional-order satisfies α?>?1. (2) In the overdamped system with single-well potential and ordinary damping, there is no resonance, whereas there is a single-resonance for the case of fractional-order damping. The necessary condition for the new result is α?>?1. (3) In the underdamped system with double-well potential and ordinary damping, there are double-resonance and one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for the new single-resonance is α?相似文献   

Bifurcation and resonance in a fractional Mathieu-Duffing oscillator

The bifurcation and resonance phenomena are investigated in a fractional Mathieu-Duffing oscillator which contains a fast parametric excitation and a slow external excitation. We extend the method of direct partition of motions to evaluate the response for the parametrically excited system. Besides, we propose a numerical method to simulate different types of local bifurcation of the equilibria. For the nonlinear dynamical behaviors of the considered system, the linear stiffness coefficient is a key factor which influences the resonance phenomenon directly. Moreover, the fractional-order damping brings some new results that are different from the corresponding results in the ordinary Mathieu-Duffing oscillator. Especially, the resonance pattern, the resonance frequency and the resonance magnitude depend on the value of the fractional-order closely.     

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.     

Vibrational resonance in a multistable system with position-dependent mass

The occurrence of vibrational resonance(VR) in a dual-frequency-driven multistable system with a spatially varying mass modelling particle with position-dependent mass(PDM) and evolving in a one-dimensional symmetric periodic potential has been investigated and reported in this paper. We numerically compute and analyze the response amplitude, the effects of the PDM parameters(m₀, a) on the potential structure, the occurrence of VR and the bifurcation of the equilibrium points. It is s...     

一类线性阻尼振子的随机共振研究

针对随机有色噪声参数激励和周期调制噪声外激励联合作用下的线性阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一、二阶稳态矩的解析表达式.发现这类系统存在传统的随机共振、广义的随机共振和“真正”的随机共振;当乘性噪声强度和调制噪声强度的比值大于等于1时,系统出现随机多共振现象.通过数值计算的系统响应功率谱,验证了理论分析结果. 关键词： 随机共振 周期调制的噪声 线性阻尼振子