p Dissipative operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of p dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrodinger operator.

Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.

The effect of the surface tension on non-propagating solitary waves

In this paper, the effect of the surface tension is considered carefully in the study of non-propagating solitary waves. The parameter plane of the surface tension and the fluid depth is divided into three regions; in two of them a breather soliton can be produced. In literature the parameters of breather solitons are all in one of the parameter regions. The new region reported here has been confirmed by our experiments. In the third region, the theoretical solution is a kink soliton, but a kind of the non-propagating solitary wave similar to the breather soliton was found in our experiments besides the kink soliton.

非传播孤立波的数值模拟

非传播孤立波是近年来由中国学者发现的一种独特的孤立水波。本文通过数值求解非传播孤立波目前公认的控制方程-Miles导出的一个带共轭项的非线性立方Schrodinger方程，对非传播孤立波进行数值模拟。本文针对非传播孤立波的各种性质，作了大量的数值计算工作，并与实验观察的现象及人们对非传播孤立波的理论研究结果进行了比较和分析。为了得到稳定的非传播孤立波，本文讨论了Miles方程中的线性阻尼系数a的值，计算表明，线性阻尼a对能否形成稳定的非传播孤立波影响很大，在某些情况下，Laedke等人提出的Miles方程的非传播孤立波解的稳定性条件与我们对Miles方程的数值模拟的结果相当一致，a可在满足稳定性条件的区间内取值，但也发现在某些情况下Laedke等人的稳定性条件与我们的数值模拟不完全符合，证明Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件，而不是充分条件。本文研究了两个非传播孤立波的相互作用，数值模拟表明，两个波的作用模式依赖于系统的参数，只有适当大小的外驱动频率和振幅及线性阻尼a可算出两个非传播孤立波周而复始的相互作用现象来，参数不合适时，两个波可能最终合并为一个非传播孤立波而不再分离，也可能彼此不发生作用，保持各自的独立。对不同的初始扰动及其演化的计算表明，要形成单个稳定的非传播孤立波，则初始扰动必须适当，否则扰动可能消失或发展成多个孤立波。关于形成非传播孤立波所需的外驱动条件，计算结果表明，只有适当大小的外驱动频率和振幅可形成稳定的非传播孤立波，数值结果可以描述驱动频率的上限和驱动振幅的上下限，但无法描述驱动频率的下限。我们的数值模拟工作说明Miles方程确实较好的描述了非传播孤立波的物理模型，该方程可以解释许多关于非传播孤立波的物理特性。但Miles方程无法对非传播孤立波的某些实验现象作出解释，因而有待于进一步研究改进。

Verification of a scaling law in few-cycle laser pulses

The scaling law of photoionization in few-cycle laser pulses is verified in this paper. By means of numerical solution of time-dependent Schrodinger equation, the photoionization and the asymmetry degree of photoionization of atoms with different binding potential irradiated by various laser pulses are studied. We find that the effect of increasing pulse intensity is compensated by deepening the atomic binding potential. In order to keep the asymmetric photoionization unchanged, if the central frequency of the pulse is enlarged by k times, the atomic binding potential should also be enlarged by k times, and the laser intensity should be enlarged by k(3) times. (c) 2005 Optical Society of America.

A scaling law of photoionization in ultrashort pulses

By means of the numerical solution of time-dependant Schrodinger equation, we verify a scaling law of photoionization in ultrashort pulses. We find that for a given carrier-envelope phase and duration of the pulse, identical photoionizations are obtained provided that when the central frequency of the pulse is enlarged by k times, the atomic binding potential is enlarged by k times, and the laser intensity is enlarged by k(3) times. The scaling law allows us to reach a significant control over direction of photoemission and offers exciting prospects of reaching similar physical processes in different interacting systems which constitutes a novel kind of coherent control.

μ^-子催化核聚变中强脉冲激光对介原子μ^3He的电离

数值求解了一维含时的Schroedinger方程，研究了μ子催化核聚变反应中激光强度和波长对介原子μ^3He电离的影响．发现当激光强度为10^19-10^23W/cm^2量级时，介原子μ^3He有2．7％左右的电离率；当激光强度达到6．0×10^24W/cm^2时，对介原子μ^3He有显著的电离，并且电离率随着激光的强度、波长而递增，进而会有效提高μ子的催化效率．

Nonlinear X-wave formation and conical emission at different powers of a femtosecond laser pulse in water

Nonlinear X-wave formation at different pulse powers in water is simulated using the standard model of nonlinear Schrodinger equation (NLSE). It is shown that in near field X-shape originally emerges from the interplay between radial diffraction and optical Kerr effect. At relatively low power group-velocity dispersion (GVD) arrests the collapse and leads to pulse splitting on axis. With high enough power, multi-photon ionization (NIPI) and multi-photon absorption (MPA) play great importance in arresting the collapse. The tailing part of pulse is first defocused by MPI and then refocuses. Pulse splitting on axis is a manifestation of this process. Double X-wave forms when the split sub-pulses are self-focusing. In the far field, the character of the central X structure of conical emission (CE) is directly related to the single or double X-shape in the near field. (c) 2007 Elsevier B.V. All rights reserved.

Transmission properties through a double quantum dot with a wave packet

The transmiss on time and tunneling probability of an electron through a double quantum dot are studied using the transfer matrix technique. The time-dependent Schrodinger equation is applied for a Gaussian wave packet passing through the double quantum clot. The numerical calculations are carried out for a double quantum clot consisting of GaAs/InAs material. We find that the electron tunneling resonance peaks split when the electron transmits through the double quantum dot. The splitting energy increases as the distance between the two quantum dots decreases. The transmission time can be elicited from the temporal evolution of the Gaussian wave packet in the double quantum dot. The transmission time increases quickly as the thickness of tire barrier increases. The lifetime of the resonance state is calculated tram the temporal evolution of the Gaussian-state at the centers of quantum dots.

A fully three-dimensional atomistic quantum mechanical study on random dopant-induced effects in 25-nm MOSFETs

A fully 3-D atomistic quantum mechanical simulation is presented to study the random dopant-induced effects in nanometer metal-oxide-semiconductor field-effect transistors. The empirical pseudopotential is used to represent the single particle Hamiltonian, and the linear combination of bulk band method is used to solve the million atom Schrodinger equation. The gate threshold fluctuation and lowering due to the discrete dopant configurations are studied. It is found that quantum mechanical effects increase the threshold fluctuation while decreasing the threshold lowering. The increase of threshold fluctuation is in agreement with the researchers' early study based on an approximated density gradient approach. However, the decrease in threshold lowering is in contrast with the density gradient calculations.

Transmission properties of electron in quantum rings

We investigated the transmission probability of a single electron transmission through a quantum ring device based on the single-band effective mass approximation method and transfer matrix theory. The time-dependent Schrodinger equation is applied on a Gaussian wave packet passing through the quantum ring system. The electron tunneling resonance peaks split when the electron transmits through a double quantum ring. The splitting energy increases as the distance between the two quantum rings decreases. We studied the tunneling time through the single electron transmission quantum ring from the temporal evolution of the Gaussian wave packet. The electron probability density is sensitive to the thickness of the barrier between the two quantum rings. (C) 2008 American Institute of Physics.

Energy Levels of Hydrogenic Impurities in InAs Quantum Ring

The distribution of energy levels of the ground state and the low-lying excited states of hydrogenic impurities in InAs quantum ring was investigated by applying the effective mass approximation and the perturbation method. In 2D polar coordinates, the exact solution to the Schrodinger equation was used to calculate the perturbation integral in a parabolic confinement potential. The numerical results show that the energy levels of electron are sensitively dependent on the radius of the quantum ring and a minimum exists on account of the parabolic confinement potential. With decreasing the radius, the energy spacing between energy levels increases. The degenerate energy levels of the first excited state for hydrogenic impurities are not relieved, and when the degenerate energy levels are split and the energy spacing will increase with the increase in the radius. The energy spacing between energy levels of electron is also sensitively dependent on the angular frequency and will increase with the increases in it. The degenerate energy levels of the first excited state are not relieved. The degenerate energy levels of the second excited state are relieved partially. The change in angular frequency will have a profound effect upon the calculation of the energy levels of the ground state and the low-lying excited states of hydrogenic impurities in InAs quantum ring. The conclusions of this paper will provide important guidance to investigating the optical transitions and spectral structures in quantum ring.

One-dimensional quantum waveguide theory of Rashba electrons

The ballistic spin transport in one-dimensional waveguides with the Rashba effect is studied. Due to the Rashba effect, there are two electron states with different wave vectors for the same energy. The wave functions of two Rashba electron states are derived, and it is found that their phase depend on the direction of the circuit and the spin directions of two states are perpendicular to the circuit, with the +pi/2 and -pi/2 angles, respectively. The boundary conditions of the wave functions and their derivatives at the intersection of circuits are given, which can be used to investigate the waveguide transport properties of Rashba spin electron in circuits of any shape and structure. The eigenstates of the closed circular and square loops are studied by using the transfer matrix method. The transfer matrix M(E) of a circular arc is obtained by dividing the circular arc into N segments and multiplying the transfer matrix of each straight segment. The energies of eigenstates in the closed loop are obtained by solving the equation det[M(E)-I]=0. For the circular ring, the eigenenergies obtained with this method are in agreement with those obtained by solving the Schrodinger equation. For the square loop, the analytic formula of the eigenenergies is obtained first The transport properties of the AB ring and AB square loop and double square loop are studied using the boundary conditions and the transfer matrix method In the case of no magnetic field, the zero points of the reflection coefficients are just the energies of eigenstates in closed loops. In the case of magnetic field, the transmission and reflection coefficients all oscillate with the magnetic field; the oscillating period is Phi(m)=hc/e, independent of the shape of the loop, and Phi(m) is the magnetic flux through the loop. For the double loop the oscillating period is Phi(m)=hc/2e, in agreement with the experimental result. At last, we compared our method with Koga's experiment. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3253752]

The quantum tunnelling between two-component Bose-Einstein condensates in a double-well configuration

We examine in terms of exact solutions of the time-dependent Schrodinger equation, the quantum tunnelling process in Bose-Einstein condensates of two interacting species trapped in a double well configuration. Based on the two series of time-dependent SU(2) gauge transformations, we diagonalize the Hamilton operator and obtain analytic time-evolution formulas of the population imbalance and the berry phase. the particle population imbalance (a(L)(+)aL - a(R)(+)a(R)) of species A between the two wells is studied analytically.

The quantum tunneling between two-component Bose-Einstein condensates in a double-well configuration

In terms of exact solution of the time-dependent Schrodinger equation. we examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We use the two series of time-dependent SU(2) gauge transformation to diagonalize the Hamilton operator obtain analytic time-evolution formulas of the population imbalance and the berry phase. The particle population imbalance (a(L)(+)a(L) - a(R)(+)a(R)) of species A between the two wells is studied analytically.