Non-Adiabatic Geometric Phase in a Dispersive Interaction System

We investigate the geometric phase and dynamic phase of a two-level fermionic system with dispersive interaction, driven by a quantized bosonic field which is simultaneously subjected to parametric amplification. It is found that the geometric phase is induced by a counterpart of the Stark shift. This effect is due to distinct shifts in the field frequency induced by interaction between different states （｜e〉 and ｜g〉 ） and cavity field, and a simple geometric interpretation of this phenomenon is given, which is helpful to understand the natural origin of the geometric phase.

Connection of Screw Instability with Electric Current in an Accretion Disc around a Black Hole

The screw instability of the magnetic field is discussed based on its poloidal configuration generated by a single toroidal electric current flowing in the equatorial plane of a Kerr black hole （BH）. The rotation of the BH relative to the disc induces an electromotive force, which in turn results in a poloidal electric current. By using Ampere＇s law, we calculate the toroidal component of the magnetic field and derive a criterion for the screw instability of the magnetic field connecting the rotating BH with its surrounding disc. It is determined that the screw instability is related to two parameters： the radius of the disc and the BH spin. The occurrence of screw instability is depicted in a parameter space. In addition, we discuss the effect of the screw instability on magnetic extraction of energy from the rotating BH.

Investigation of Properties of Motion of Superconductive Electrons in Superconductors by Nonlinear Quantum Mechanical Theory

The properties and rules of motion of superconductive electrons in steady and time-dependent non-equilibrium states of superconductors are studied by using the Ginzberg-Landau （GL） equations and nonlinear quantum theory. In the absence of external fields, the superconductive electrons move in the solitons with certain energy and velocity in a uniform system, The superconductive electron is still a soliton under action of an electromagnetic field, but its amplitude, phase and shape are changed. Thus we conclude that superconductivity is a result of motion of soliton of superconductive electrons. Since soliton has the feature of motion for retaining its energy and form, thus a permanent current occurs in superconductor. From these solutions of GL equations under action of an electromagnetic field, we gain the structure of vortex lines-magnetic flux lines observed experimentally in type-Ⅱ superconductors. In the time-dependent nonequilibrium states of superconductor, the motions of superconductive electrons exhibit still the soliton features, but the shape and amplitude have changed. In an invariant electric-field, it moves in a constant acceleration. In the medium with dissipation, the superconductive electron behaves still like a soliton, although its form, amplitude, and velocity are altered. Thus we have to convince that the superconductive electron is essentially a soliton in both non-equilibrium and equilibrium superconductors.

Principle, system, and applications of tip-enhanced Raman spectroscopy

Raman spectroscopy is a powerful technique in chemical information characterization. However, this spectral method is sub- ject to two obstacles in nano-material detection. One is diffraction limited spatial resolution, and the other is its inherent small Raman cross section and weak signaling. To resolve these problems, a new approach has been developed, denoted as tip-enhanced Raman spectroscopy （TERS）. TERS is capable of high-resolution and high-sensitivity detection and demonstrat- ed to be a promising spectroscopic and micro-topographic method to characterize nano-materials and nanostructures. In this paper, the principle and experimental system of TERS are discussed. The latest application of TERS in molecule detection, bi- ological specimen identification, nanao-material characterization, and senti-conductor material determination with some spe- cific experimental examples are presented.