Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

On the validity of the counterpoise correction for the basis set superposition error including the fragment relaxation terms

It is demonstrated that relatively large geometrical changes make Emsley et al.'s assumption (J Am Chem Soc (1978) 100:3303) on the counterpoise correction for the basis set superposition error including the fragment relaxation terms unacceptable. Received: 23 September 1997 / Accepted: 31 October 1997     

Polarization of coherent synchrotron radiation from an electron beam rotating in a plasma

After eliminating reflections from the walls of the plasma container, we observed polarization of the coherent synchrotron radiation from a relativistic electron beam rotating in a plasma. Several features of the polarization agree well with calculations based on the single particle synchrotron radiation theory. A particular polarization ratio (Fig. 3) does not, however. We deduce from this direct diffraction of the radiation by the beam electrons. This is strong evidence for beam-particle bunches of size cm. Also, there must be some absorption of the extraordinary wave to account for the observations. We suggest a way to apply these results to measure the pitch angle of the beam.Work supported by Army Research Office.     

Review of chip-scale atomic clocks based on coherent population trapping

Research on chip-scale atomic clocks （CSACs） based on coherent population trapping （CPT） is reviewed. The back- ground and the inspiration for the research are described, including the important schemes proposed to improve the CPT signal quality, the selection of atoms and buffer gases, and the development of micro-cell fabrication. With regard to the re- liability, stability, and service life of the CSACs, the research regarding the sensitivity of the CPT resonance to temperature and laser power changes is also reviewed, as well as the CPT resonance＇s collision and light of frequency shifts. The first generation CSACs have already been developed but its characters are still far from our expectations. Our conclusion is that miniaturization and power reduction are the most important aspects calling for further research.     

不同光场二阶相干度的实验研究

基于Hanbury Brown-Twiss(HBT)实验,我们借助于两个单光子计数模块,一个50/50分束器和一个快速计数卡(FastCom-P7888)研究了不同光场的二阶相干度。我们首先制备了脉冲相干光,连续相干光以及单原子发出的单光子源,并测量这几种不同光场的二阶相干度g(2)(τ)。我们通过测量俘获在磁光阱(MOT)和远失谐偶极阱(FORT)中的单原子在近共振连续激光激发下所辐射的荧光的二阶相干度,分别得到了g(2)(τ=0)=0.08和g(2)(τ=0)=0.09,借助于实验中产生的脉冲光与单原子,接下来我们将进行触发式单光子源的实验研究。     

On a hidden symmetry of quantum harmonic oscillators

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented.     

Detection on micro-Doppler effect based on 1550 nm laser coherent radar

A laser coherent detection system of 1550 nm wavelength was presented, and experimental research on detecting micro-Doppler effect in a dynamic target was developed. In this paper, the return signal in the time domain is decomposed into a set of components in different wavelet-scales by multi-resolution analysis, and the components are associated with the vibrational motions in a target. The micro-Doppler signatures are extracted by applying the reconstruction (inverse wavelet transform). During the course of the final data processing frequency analysis and time–frequency analysis are applied to analyze the vibrational signals and estimate the motion parameters successfully. The experimental results indicate that the micro-Doppler information in a moving can be effectively detected, and tiny vibrational signatures also can be acquired effectively by wavelet multi-resolution analysis and time–frequency analysis.     

Hypercomplex analysis and integration of systems of ordinary differential equations

We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of hypercomplexification, which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati‐type systems, we obtain invariants of Abel‐type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd.