The KP theory and Mach reflection

Interactions of two line solitons in the two-dimensional shallow-water field are studied based on the Kadomtsev–Petviashvili (KP) theory. With the use of the normal form, the extended KP equation with higher-order correction is derived. This extended KP theory improves significantly the predictability of the original KP theory for soliton interactions with finite oblique angles. The previously existing discrepancy between the experiments and the theory in the Mach reflection problem is now resolved by the normal form theory.

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Feynman’s path integral reformulates the quantum Schrödinger differential equation to be an integral equation. It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems. In this Review, the molecular Schrödinger equation will first be introduced, together with the Born-Oppenheimer approximation that decouples electronic and internuclear motions. Some effective semiclassical potentials, e.g., centroid potential, which are all formulated in terms of Feynman’s path integral, will be discussed and compared. These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger’s energy eigenvalues. As a result, path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques. To complement these techniques, we will examine how Kleinert’s variational perturbation (KP) theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential. To enable the powerful KP theory to be practical for many-body molecular systems, we have proposed a new path-integral method: automated integration-free path-integral (AIF-PI) method. Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method, we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions. The computational procedure of using our AIF-PI method, along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy (AMAZE), are also highlighted in this review.

Optical Properties of Quantum Dashes

There are presented optical properties of strongly in-plane elongated nanostructures the so called quantum dashes made in InAs/InP material system by molecular beam epitaxy. They have been investigated systematically by a spectroscopic manner on both the entire ensemble and on the single dash level. Their properties are discussed with respect to the fundamental electronic and optical properties as the polarization of emission and the corresponding driving factors, exciton fine structure splitting, biexciton binding energy, the characteristic exciton to biexciton lifetimes ratio and exciton decoherence via interaction with acoustic phonons. The experimental results are analyzed supported by previous energy level calculations within the eight-band kp theory and the rate equation modeling of the exciton kinetics.

Anisotropic Hole Mobility in Strained Si1-xGex/(001)Si

Applying KP theory combined with deformation potential we obtained the valence band structure, and based on this result we calculated the orientation-dependent effective mass which is also called conductivity effective mass in strained Si1-xGex/(001)Si in this research, and furthermore ,we established the scattering rate model by using the density-of-states effective mass. On the basis of conductivity effective mass and scattering rate model, utilizing analytical method and relaxation time approximation we obtained the dependence of the value of hole mobility on stress and doping concentration in strained Si1-xGex/(001)Si along different crystal orientations. Compare to the unstrained Si, the anisotropy of hole mobility is more obvious in strained Si1-xGex/(001)Si, for example, It shows that under the same stress and doping concentration (Ni=1x1014cm-3, x=0.4), the value of hole mobility along [010] crystal orientation is visibly higher than other crystal orientations. This result can provide valuable references to the research of hole mobility of strained Si1-xGex materials and the design of devices.

Electron Mobility Model of Strained Si1-xGex(001)

Solving the Schrödinger equation with strain Hamiltonian and combining with KP theory, we obtained the conductivity effective mass and density of states effective mass of strained Si1-xGex(001) in this paper. On the basis of conductivity effective mass and density of states effective mass, considered of Fermi golden rule and Boltzman collision term approximation theory, scattering rate model was established in strained Si1-xGex(001). Based on the conductivity effective mass and scattering rate models we discussed the dependence of electron mobility on stress and doping concentration in strained Si1-xGex(001), it shows that electron mobility decrease with the increasing of stress and doping concentration. This result can provide valuable references to the research of electron mobility of strained Si1-xGexmaterials and the design of devices.

INTERSECTING D-BRANE STATES DERIVED FROM THE KP THEORY

A general scheme to find string boundary states is developed within the framework of the theory of KP hierarchy. The method is applied to calculate correlation function of intersecting D-branes and rederived from the results of our previous works as special examples. A matrix generalization of this scheme provides a method to study dynamics of coincident multi D-branes.