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.     

Deterministic chaos in one-dimensional maps—the period doubling and intermittency routes

This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.     

First-principles studies of the vibrational properties of amorphous carbon nitrides

Raman spectra of amorphous carbon nitride films (a-C:N) resemble those of typical amorphous carbon (a-C), and no specific features in the spectra are shown due to N doping. The present work provides a correlation between the microstructure and vibrational properties of a-C:N films from first principles. The six periodic model structures of 64 atoms with various mass densities and nitrogen contents are generated by the liquid-quench method using Car-Parinello molecular dynamics. By using Raman coupling tensors calculated with the finite electric field method, Raman spectra are obtained. The calculated results show that the vibrations of C=N could directly contribute to the Raman spectrum. The similarity of the Raman line shapes of N-doped and N-free amorphous carbons is due to the overlapping of C=N and C=C vibration bands. In addition, the origin of characteristic Raman peaks is also given.     

First-principles study on the geometric and electronic structures and phase transition of PbZr1-xTixO3 solid solutions

With first-principles virtual-crystal approximation calculations, we systematically investigate the geometric and elec- tronic structures as well as the phase transition of lead zirconate titanate (PbZr1-xTixO3 or PZT) as a function of Ti content for the whole range of 0 ≤ x Ti ≤ 1. It can be found that, with the increase of the Ti content, the PbZr1-xTixO3 solid solu- tions undergo a rhombohedral-to-tetragonal phase transition, which is consistent with the experimental results. In addition, we also show the evolution in geometric and electronic structures of rhombohedral and tetragonal PbZr1-x TixO3 with the increasing content of Ti.     

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.     

介质膜滤波器色散特性的研究

采用信号处理的方法,对介质膜滤波器的滤波特性进行了详细的研究。介质膜滤波器是最小相位滤波器,它的幅度响应与相位响应之间存在希尔伯特变换规律,因此可以通过它的幅度响应重构它的相位响应,进而可以得到它的色散特性。为了验证理论分析,设计了射频调制法测试介质膜滤波器群速度延时的实验装置。实验测试了一个100GHz33信道的介质膜滤波器的群速度延迟。通过对实验结果与理论计算结果的对比分析,发现实验数据与理论分析吻合得比较好。最后,对介质膜滤波器的色散的特点进行了分析。     

First-principles study on the electronic structures of iron phthalocyanine monolayer

The electronic band structure and magnetic properties of iron phthalocyanine (FePc) monolayer were investigated by using the first-principles all-electron full-potential linearized augmented plane wave energy band method. It is found that the ferromagnetic FePc monolayer is energetically more stable than the paramagnetic one. The exchange interaction, which splits the majority and minority bands, influences strongly on the electronic structure near the Fermi level (E_F). Magnetic moment of the central Fe atom is calculated to 1.95 μ_B. The range of the positive polarization of Fe site is larger in the out-of-plane than in the in-plane direction. The FePc ligand remains paramagnetic. The presence of states at E_F indicates the metallic character of FePc monolayer both for the paramagnetic and ferromagnetic states. However, the large density of states at E_F of the majority spins in the ferromagnetic state is expected to cause a phase transition to insulating antiferromagnetic state from the metallic ferromagnetic one.     

Surface core level shift observed on NiAl(1 1 0)

Using high resolution core level spectroscopy, a surface core level shift towards lower binding energy of −0.13 eV is determined for the 2p level of the outwardly relaxed Al surface atoms on NiAl(1 1 0). Density functional theory based calculations with inclusion of final state effects yield a value of −0.14 eV for this shift in excellent agreement with experiment. We show that the initial state approximation yields a value of +0.09 eV, i.e. the inclusion of final state relaxation effects is vital not only to obtain the correct value but even the correct sign for this shift.     

String Cosmological Solutions with O(d,d) Duality Symmetry and Matter Coupling

The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.