Radiative decay from doubly to singly excited states of He via generalization of Laguerre-type orbitals： A non-orthogonal formalism

By taking full account of the non-orthogonality of the orbitals between the low-lying doubly excited states ^1po and the singly excited states ^1S^e and ^1D^e of He, the corresponding radiative decay rates have been investigated theoretically via analytic generalized Laguerre-type atomic orbitals at a nearly numerical multi-conflguration self-consistent field accuracy in a general non-orthogonal configuration interaction scheme. From these rates, we calculate the VUV photon emission and metastable atom spectra, and both are found to be in good qualitative agreement with recent excellent measurements. We obtain, successfully, the enhancement of the VUV photon spectrum, experimentally observed at the energy of （2s4p-4s2p）/（2p,3d） ^1po as compared with other nearby lying states. The mechanism proposed by Odling-Smee et al is verified, implying that taking appropriate account of the overlap existing between orbitals of the low-lying doubly excited and singly excited states （especially important for the compact orbitals） can reveal basic physical dominant mechanism and is crucial in understanding these spectra.

Infinitely Many Symmetries of Konopelchenko-Dubrovsky Equation

A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra.

Phonon-dependent transport through a serially coupled double quantum dot system

Using Keldysh nonequilibrium Green function formalism and mapping a many-body electron-phonon interaction onto a one body problem, the electron transport through a serially coupled double quantum dot system is analyzed. The influence of the electron-phonon interaction, temperature, detuning, and interdot tunneling on the transmission coefficient and current is studied. Our results show that the electron-phonon interaction results in the appearance of the side peaks in the transmission coefficient, whose height is strongly dependent on the phonon temperature. We have also found that the inequality of the electron-phonon interaction strength in two dots gives rise to an asymmetry in the current-voltage characteristic. In addition, the temperature difference between the phonon and electron subsystems results in the reduction of the saturated current and the destruction of the step-like behavior of the current. It is also observed that the detuning can improve the magnitude of the current by compensating the mismatch of the quantum dots energy levels induced by the electron-phonon interaction.

New Extended Jacobi Elliptic Function Rational Expansion Method and Its Application

In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the （2＋1）-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations.

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to （2＋1）-Dimensional Stochastic Dispersive Long Wave System

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the （2＋ 1）-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

Negative differential resistance in molecular devices: the role of molecule-electrode coupling

By applying nonequilibrium Green's function formalism combined with the first-principles density functional theory, we investigate the electronic transport in two molecular junctions constituted by a substituted oligo (phenylene ehtynylene) sand-wiched between two Au electrodes. Our calculations show that the weak molecule-electrode coupling is responsible for the observation of the negative differential resistance (NDR) effect in experiments. When the coupling is weak, the projected density of states (PDOS) of the molecule and the electrodes undergoes a mismatch-match-mismatch procedure, which increases and then decreases the transmission peak intensities, leading to a NDR effect. We also find that the localization/delocalization of the molecular orbitals and the change of charge state of the molecule have no direct relation with the NDR effect, because they change little as the voltage increases.