Fine structure of splitting of the separatrix of a nonlinear resonance

This report is a continuation of an analysis, initiated elsewhere V.V. Vecheslavov and B. V. Chirikov, Zh. éksp. Teor. Fiz. 114, 1516 (1998) [JETP 86, 823 (1998)], of the effect of splitting of the separatrix of a nonlinear resonance for the model of standard mapping, based on results of direct measurements of the splitting angle α(K), where K is the system parameter. Measurements were made in the previously used wide range 0.1≳α≳10⁻²⁰⁸ (1⩾K⩾0.0004), but with significantly higher relative (better than 10⁵⁰) and average (∼10⁻⁵⁵) accuracy. This procedure made it possible to substantially refine the effects observed in Ref. 1 and construct qualitatively new empirical dependences providing reliable extrapolation of the data obtained for the angle and the invariant in the intermediate asymptotic limit K≲10⁻² beyond the limits of the investigated region. The results obtained by us can be useful for further development of the theory of separatrix splitting and formation of the stochastic layer of a nonlinear resonance. Zh. éksp. Teor. Fiz. 116, 336–346 (July 1999)     

Resonant drift-wave coupling modified by nonlinear separatrix dissipation

Resonant drift-wave coupling experiments characterize a new dissipative coupling term caused by a trapping separatrix. The system is a cylindrical pure-electron plasma with an axial trapping separatrix generated by an applied theta-symmetric wall voltage. The resonant decay of m_{theta}=2 diocotron modes into m_{theta}=1 trapped-particle diocotron modes is measured and compared to parametric mode coupling theory. Experiments quantify the traditional nonlinear mode coupling term, plus a new separatrix-generated dissipative coupling term which is not yet characterized theoretically.     

空间环境高精度光电轴角测量研究

在复杂恶劣的气候条件下进行高精度的轴角测量已经成为发展空间应用技术的主要瓶颈,其中空间温度交变和振动环境,严重制约着空间用轴角测量装置的精度和使用寿命。分析了空间应用环境造成光电轴角测量装置输出误码和器件老化机理,提出一种在空间复杂环境进行高精度轴角测量的系统解决方案。给出了系统硬件设计方法,并采用了一种码盘信号自适应处理技术,弥补了传统的光电轴角测量方法的缺陷,在保证轴角测量高精度的前提下,提高了空间测角平台的可靠性和使用寿命。实验结果表明：测角分辨率为0.618″;测角误差峰-峰值为6.2″。     

Evidence of Autler-Townes splitting in high-order nonlinear processes

We demonstrate Autler-Townes (AT) splitting of four-wave mixing in an electromagnetically induced transparency window, which results from the destructive interference between a three-photon process and a five-photon process. The primary and secondary AT splittings are achieved via induced atomic coherence in a four-level Y-type atomic system. Theoretical calculations fit well with the experimentally measured results. Such controlled multichannel splitting of nonlinear optical signals can have potential applications in optical communication and quantum information processing.     

Quantum-electrodynamical photon splitting in magnetized nonlinear pair plasmas

We present for the first time the nonlinear dynamics of quantum electrodynamic (QED) photon splitting in a strongly magnetized electron-positron (pair) plasma. By using a QED corrected Maxwell equation, we derive a set of equations that exhibit nonlinear couplings between electromagnetic (EM) waves due to nonlinear plasma currents and QED polarization and magnetization effects. Numerical analyses of our coupled nonlinear EM wave equations reveal the possibility of a more efficient decay channel, as well as new features of energy exchange among the three EM modes that are nonlinearly interacting in magnetized pair plasmas. Possible applications of our investigation to astrophysical settings, such as magnetars, are pointed out.     

High-precision measurement of the 14O half-life using a mass-separated radioactive beam

A high-precision measurement of the ¹⁴O half-life has been performed using a mass-separated radioactive beam in combination with a germanium detector set-up. This is the first ¹⁴O half-life measurement with a contamination-free source. The final result of 70.560 ± 0.049 seconds is in agreement with the generally adopted mean value. Received: 5 April 2001 / Accepted: 6 August 2001     

球面镜真空紫外光谱反射率的高精度测量

为了实现对球面镜真空紫外光谱反射率的直接测量,构建了一套真空紫外光谱反射率测试系统。该系统以氟化镁窗口氘灯与Seya-Namioka凹面光栅单色仪产生单色光源,反射式调制器与参考探测器做光学补偿,内径80mm的荧光积分球与精密转台作为接收系统。光学补偿消除单色光源不稳定性,荧光积分球消除了两次测量光斑不同对探测器响应的影响,且减少了系统的能量损失。利用该系统测量了115～180nm球面镜的反射率,测试结果表明测量重复性优于±0.3%;按国际通用不确定度评估规范,对系统进行不确定度分析,相关不确定度小于1.3%。实现了球面镜反射率的高精度测量。     

Quantum nonlinear resonance in a strong electromagnetic field

The motion of a one-dimensional quantum weakly anharmonic system under the influence of harmonic external field is treated in the range where the transition frequency between the neighboring levels is close to the frequency of the harmonic field (quantum nonlinear resonance). The case of the strong external field, in which the Rabi frequency for the transitions is large in comparison with the field frequency, is studied. The expression for compact wavepackets of quasienergy states that change their content and width periodically (and, possibly, strongly), is obtained.     

Forced nonlinear resonance in a system of coupled oscillators

We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t～?(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.     

Stability of two-mode internal resonance in a nonlinear oscillator

We analyze the stability of synchronized periodic motion for two coupled oscillators, representing two interacting oscillation modes in a nonlinear vibrating beam. The main oscillation mode is governed by the forced Duffing equation, while the other mode is linear. By means of the multiple-scale approach, the system is studied in two situations: an open-loop configuration, where the excitation is an external force, and a closed-loop configuration, where the system is fed back with an excitation obtained from the oscillation itself. The latter is relevant to the functioning of time-keeping micromechanical devices. While the accessible amplitudes and frequencies of stationary oscillations are identical in the two situations, their stability properties are substantially different. Emphasis is put on resonant oscillations, where energy transfer between the two coupled modes is maximized and, consequently, the strong interdependence between frequency and amplitude caused by nonlinearity is largely suppressed.     

Suppression of chaos in the vicinity of a separatrix

The standard Melnikov method for analyzing the onset of chaos in the vicinity of a separatrix is used to explore the possibility of suppressing chaos of dynamical systems of a certain class. Analytical expressions are obtained for external perturbations that eliminate chaotic behavior. These results are supplemented with a numerical analysis of the Duffing-Holmes-oscillator and pendulum equations.     

Anomalous magnetic splitting of the kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in a finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for a nonzero magnetic field and the Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulas are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large- N approaches to spin- 1 / 2 impurities at finite magnetic field is suggested.     

Smale's horseshoe map in a Hamiltonian system around a separatrix

A non-linear system with one degree of freedom is studied. It is assumed that the potential of the system is a double-well type and that a time-dependent external field is imposed on the system as a perturbation. The analytic solutions around a separatrix are obtained using the first order perturbation. These analytic solutions are in good agreement with the numerical integrations. It is further shown that these solutions draw a horseshoe map of the Smale type.     

Exciton splitting and Fermi resonance in solid solutions

Experimental investigations of the exciton spectra in CH₃I:CD₃I mixed crystals in the Fermi resonance region are made on the well oriented polycrystalline samples. The results obtained are compared with the theory developed.     

High-precision index measurement in anisotropic crystals using white-light spectral interferometry

White-light spectral interferometry appears an excellent tool for precise determination of indices, and has already been successfully applied to different isotropic or weakly dispersive materials such as glass or rhodamine films. In this paper, we extend the spectral method to the measurement of anisotropic media with strong dispersion. The method is discussed below and allows an accuracy of the order of 10^-5 on the principal indices of a birefringent silver thiogallate (AgGaS₂) crystal.     

Internal nonlinear resonance on a charged jet

Nonlinear analytical asymptotic calculations of the second order of smallness show that the motion of a charged jet in a material medium generates periodic wave motions of the jet-medium interface (Kelvin-Helmholtz instabilities), which grow in time. In addition, the motion of the jet gives rise to nonlinear internal resonance interaction of waves. The parameters of this interaction (intensity and characteristic time) depend on the physical parameters of the system: electric charge density of the jet, its velocity in the medium, mass density, wavenumbers of interacting waves, and the interfacial tension coefficient.