共面两囚禁离子体系精确的量子运动

研究Paul阱中共面两离子体系精确的量子运动. 在考虑库仑关联的条件下，得到了系统Schr?dinger方程的精确解和以此为基础的微扰解，包括精确的离散本征态和本征能量，以及近似的分段连续谱和能带结构. 以低能级的几个态为例，用数值方法计算了两离子间的平均距离，并绘出了两离子的概率分布图. 关键词： Paul阱 共面两离子 平均距离 能带结构     

Paul阱中一维两离子系统的能带结构

利用熟知的级数截断方法，设计数值程序计算了线形Paul阱中库仑关联的两离子系统Schrdinger方程的精确解，得到接近目前离子阱实验能够实现的阱频下系统分立的运动态波函数和能谱，它们对应于阱频值的一个无穷可数的点集.在该点集内两相邻点之间连续变化阱频，由量子微扰法得到以精确分立谱为基础的能带结构，包括较宽的能隙和较窄的带宽.能带结构的存在将影响以该系统为基础的量子逻辑操作和激光边带冷却等问题，应该在实验研究中加以考虑.     

激光脉冲作用下囚禁离子的规则与混沌运动

研究驻波型激光脉冲作用下，失谐量足够大时，囚禁于Paul阱中的单离子系统的久期运动.通过分析和数值计算相结合的方法，导出系统的精确解及其描述的时间演化性质，得到系统的规则和混沌运动轨道以及阱频很小时系统进入整体混沌的临界条件,并提出了控制系统共振失稳的方法. 关键词： 激光脉冲 囚禁离子 规则与混沌运动 精确解 稳定性     

囚禁单个和两个共面超冷离子的Penning阱系统的量子力学求解

分别求解囚禁了一个和两具共面超冷离子的Ｐｅｎｎｉｎｇ阱系统的薛定谔方程。     

Paul阱中存储离子的研究

根据Paul离子阱结构及电场分布特点,列出阱内离子运动方程并求解,对其中离子运动、硅团簇离子碰撞解离反应进行了分析.     

离子阱中共线两离子基本量子逻辑门的实现

运用量子理论,在Paul阱中共线两离子系统的精确解的基础上,结合量子编码方法,讨论了囚禁两离子系统量子非门(单比特逻辑非门、两比特逻辑非门)实现的理论方法,提出利用质心振动模和两离子构建量子与门的理论方法(不需第三个离子),通过分析,证明了囚禁两离子系统在相对量子数l=1时,可制备为单比特量子非门和量子与门的线性叠加,可以完成并行量子逻辑操作,量子非门和量子与门是构成量子计算机制基本结构单元,值得我们在量子信息实验研究中加以考虑.     

Paul阱中离子运动及稳定性分析

Paul离子阱由于没有外加磁场所引起的塞曼效应的影响,已成为离子存储及研究离子的重要装置.根据在实验中所采用的Paul离子阱结构及电场分布特点,列出阱内离子运动方程并进行求解,对其中各种运动进行分析,同时还分析了离子存储稳定性.最后对所作的研究进行总结,得到如下结论:阱中离子的运动为谐振运动、基频微运动和高阶微振动.     

非谐射频阱中离子云系统的精确周期解

射频阱中离子云与检测场的相互作用由周期驱动的Duffing方程描述.本文报道了该方程的一个精确的周期解,它描述了阱参数和外场对离子云周期运动的影响.结果表明,在各参变量满足周期解条件时,离子的运动频率为外场频率的三分之一,运动振幅分别与外场频率、振幅以及阱频正相关,与离子阱的非谐参数反相关.     

双δ激光脉冲作用下Paul阱中单离子的规则与混沌运动

考虑赝势近似下囚禁于Paul阱中的单离子与双δ脉冲型周期势相互作用系统的规则与混沌运动.应用积分方程方法得到系统的经典运动精确解,通过数值方法作出相空间轨道图和平均能量的时间演化曲线.结合分析与数值结果,发现两个有趣的结论.即在离子与单δ脉冲作用出现共振失稳的情形,在双δ脉冲作用下却出现了稳定的规则运动;离子随着双δ脉冲中两个脉冲之间的时间间隔减小而由规则运动转为混沌运动,其平均能量扩散的快慢与混沌运动的混乱程度相关.还研究了系统的共振失稳,发现通过 关键词： 双δ脉冲 囚禁离子 精确解 混沌     

Paul阱中两个Bi+共线的能量本征态性质

通过对Paul阱中共线两Bi 形成的系统波函数、能谱和相对距离的平均值的精确计算,计算得到的频率、能量是目前的离子阱实验能达到的值;并且对共线两个Bi 的相对几率分布和系统能量本征态进行分析.     

Pseudospin Symmetry in Position-Dependent Mass Dirac-Coulomb Problem by Using Laplace Transform and Convolution Integral

The exact pseudospin symmetry solutions of Dirac equation with position-dependent mass (PDM) Coulomb potential in the presence of Colulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are given. By using Laplace convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

Similarity Reductions for a Nonlinear Diffusion Equation

Abstract

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method.     

Calculation of self-sputtering spectra of thin films by the discrete flow method

Self-sputtering of plane-parallel layers is described theoretically on the basis of the invariant immersion method combined with the discrete flow technique. Differential equations are derived for forward and backward self-sputtering functions, and exact solutions to these equations are obtained. Energy distributions of self-sputtered ions are calculated; total self-sputtering coefficients are compared to the results of computer experiment. The dependences of the total self-sputtering coefficients on the film thickness and the initial energy of ions are analyzed.     

A Modified Thermodynamics Method to Generate Exact Solutions of Einstein Equations

We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy, which is used in the original methods, and then several exact solutions of Einstein equations are obtained, including the black hole solution which is surrounded by quintessence. Moreover, the geometry surface gravity defined by Komar mass is also constructed.Secondly, we use both the Komar mass and the ADM mass to modify such method, and the similar results are obtained.Moreover, with some generalize addition to the definition of the ADM mass, our method can be generalized to global monopole spacetime.     

Calculation of the Storage Time of the Ions Confined in a Paul Trap

A Brownian motion model for the energy of the ions trapped in the pseudopotential well of a Paul trap is proposed and the exact solutions of the storage time in terms of the mean first passage time (MFPT) in the cases of white noises and colored noises are theoretically calculated. The relationships with the damping coefficient, noise parameters and the energy distribution of the ions are also discussed.     

用超对称性和形不变性方法求解环形振子的能谱和波函适

运用超对称性和形不变性方法计算环形振子的能量本征值和本征波函数. 所得到的能谱公式与用费曼路径积分方法得到的严格解完全一致.     

Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire

This letter applies energy balance method and variational iteration method to a nonlinear oscillation of a mass attached to a stretched wire. Comparison of the period of oscillation and obtained solutions with the exact one shows that both methods are very effective and convenient and quite accurate to nonlinear engineering problems.     

Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions

The classical φ⁶-field theory in (1+1) dimensions, is considered as a model for the first order structural phase transitions. The equation of motion is solved exactly; and the presence of domain wall (kink) solutions at and below the transition point, in addition to the usual phonon-like oscillatory solutions, is demonstrated. The domain wall solutions are shown to be stable, and their mass and energies are calculated. Above the transition point there exists exotic unstable kink-like solutions which takes the particle from one hill top to the other of the potential. The partition function of the system is calculated exactly using the functional integral method together with the transfer matrix techniques which necessitates the determination of the eigenvalues of a Schrödinger-like equation. Thus the exact free energy is evaluated which in the low temperature limit has a phonon part and a contribution coming from the domain wall excitations. It was shown that this domain wall free energy differs from that calculated by the use of the domain wall phenomenology proposed by Krumhansl and Schrieffer. The exact solutions of the Schrödinger-like equation are also used to evaluate the displacement-displacement, intensity-intensity correlation functions and the probability distribution function. These results are compared with those obtained from the phenomenology as well as the φ⁴-field theory. A qualitative picture of the central peak observed in structural phase transitions is proposed.     

Small polaron mass with a long range density-displacement type interaction

In this work renormalization of the effective mass of an electron due to a small polaron formation is studied within the framework of the extended Holstein model. It is assumed that an electron moves along the one-dimensional chain of ions and interacts with ions vibrations of a neighboring chain via a long-range density-displacement type force. By means of the exact calculations a renormalized mass of a nonadiabatic small polaron is obtained at strong coupling limit. The obtained results compared with the mass of small polaron of ordinary Holstein model. The effect of ions vibrations polarization on the small polaron mass is addressed.