中性粒子在Ioffe阱中的经典运动方程的Floquet解

研究中性粒子在Ioffe阱中近原点区域的囚禁时,阱中的磁场可以呈现出一种简明的形式.磁矩μ反平行于磁场的中性粒子在阱中与磁场发生相互作用,借助相互作用势,可以获得粒子在阱中的经典运动方程.在一定的条件下,采用迭代近似的目的,将方程演化为马丢方程的形式,利用传统的WKBJ目的可实现方程的近似求解.研究阱中中性粒子的囚禁问题时,感兴趣的是马丢方程的Floquet解,即周期为π,2π的全周期和半周期解,欲获得这种周期解,马丢方程中的参数λ和q必须满足一定的关系,为此必须选择阱的特定参数和粒子的特定初始条件,对这一问题进行了探索性的研究.     

The Quantum Motion of an Ion in a Combined Trap

The invariant formulation is used to investigate the quant um motion of an ion in a combined trap. The classical correspondence of the quantum motion and stability problem are then discussed.     

二维六角晶体材料中的Dirac 电子

本文综述由碳、硅、硼氮和二硫化钼等单元素或双元素构成的二维六角晶体材料中Dirac 电 子的研究成果与最新进展。文章从引言开始,接着介绍这些二维六角晶体材料的空间结构和基本 电子性质;然后探讨外场调控下这些材料在能谱和光吸收、量子输运、激子凝聚和热Josephson 效 应,以及拓扑量子相变等方面所表现出来的新奇的物理现象、简要的理论处理和可能的应用前景; 最后给出二维六角晶体材料相关研究的总结和展望。谨以本文献给南京大学建立物理学科100 周 年。     

曲线运动中的相对静止

讨论物体在曲线运动中的相对静止，提出转动参照系中几种角速度之间的关系式。     

Coupled Two-Dimensional Atomic Oscillation in an Anharmonic Trap

In atomic dynamics,oscillation along different axes can be studied separately in the harmonic trap. When the trap is not harmonic, motion in different directions may couple together. In this work, we observe a twodimensional oscillation by exciting atoms in one direction, where the atoms are transferred to an anharmonic region. Theoretical calculations are coincident to the experimental results. These oscillations in two dimensions not only can be used to measure trap parameters but also have potential applications in atomic interferometry and precise measurements.     

Structure and Spectrum of Binary Classic Systems Confined in a Parabolic Trap

The static and dynamic properties of the two-dimensional classic system of two-species interacting charged particles in a parabolic trap are studied. The ground state energy and configuration for different kinds of binary systems are obtained by Monte Carlo simulation and Newton optimization. The spectrum and normal modes vectors can be gained by diagonalizing the dynamical matrix of the system. It is found that the total particle number, particle number and mass-to-charge ratio of each species are decisive factors for the system structure and spectrum. The three intrinsic normal modes of single species Coulomb clusters are inherent, concluded from our numerical simulations and analytical results.     

Three Charged Bosons Confined in a Harmonic Trap

A system of three charged bosons confined in a harmonic trap has been investigated by an exact diagonalization. We report a calculation for the energy spectrum of the low-lying states of a system of three charged bosons.The important feature of the low-lying states of three charged bosons in a harmonic trap is obtained via an analysis of the energy spectrum.     

Three Charged Bosons Confined in a Harmonic Trap

A system of three charged bosons confined in a harmonic trap has been investigated by an exact diagonalization. We report a calculation for the energy spectrum of the low-lying states of a system of three charged bosons. The important feature of the low-lying states of three charged bosons in a harmonic trap is obtained via an analysis of the energy spectrum.     

Interaction of Twisted Light with Electrons in Two-Dimensional Quantum Rings

We investigate the dynamics of charge carriers propagating in a ring being induced by twisted light: The exciting laser beam is assumed to have nonzero orbital angular momentum. The selection rules for the transitions between the eigenstates of the two-dimensional ring are determined with the aid of analytic and numerical methods. Using these results, we gain an insight into the physical process that leads to the transfer of the angular momentum of the laser beam to the electrons in the quantum ring.     

Klein Paradox of Two-Dimensional Dirac Electrons in Circular Well Potential

We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.     

Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.     

中性粒子在Ioffe阱中的经典运动

Ioffe阱因能对中性粒子实现稳定囚禁而成为一种倍受关注的磁阱。若只讨论阱中的近原点区域时,阱中的磁场可以呈现出一种简明的形式。磁矩μ反平行于磁场的中性粒子在阱中与磁场发生相互作用,借助相互作用势,可以获得粒子在阱中的经典运动方程。本文着重探究这种方程的近似求解方法。在一定的条件下,我们可以采用逐次近似的方法,使方程演化为我们熟悉的马丢方程的形式。若阱的参数设置使得马丢方程中λ>>q>0成立时,我们可以利用传统的WKBJ方法近似求解马丢方程。作为一种新的尝试,本文还采用傅立叶级数展开的办法来对马丢方程进行求解,从而得到中性粒子在阱中的经典运动规律。     

三种多环芳烃混合溶液二维荧光相关谱解析

多环芳烃为优先控制污染物,但是由于其含量很低,多组分多环芳烃荧光峰相互重叠,所以常规荧光光谱法无法对其荧光峰进行有效解析。采用二维荧光相关分析方法对三种多环芳烃,蒽、菲和芘的混合溶液进行荧光峰解析。根据研究目标,按照三种多环芳烃浓度比的不同配制了三种混合物体系,共27个样本,每种体系的三种溶液浓度彼此间按规律递增和递减。在此基础上,以浓度为外扰,构建了各体系的同步和异步二维荧光相关谱。同步谱中,在425,402,381,373,365,393及347 nm处产生自相关峰。以未被覆盖的菲在347 nm处荧光峰为线索,通过其与各波长处荧光交叉峰的正负,判断出了402,381,425和452 nm处荧光峰源于混合溶液中的蒽; 373与393 nm处荧光峰源于混合溶液中的芘; 365,356及347 nm处荧光峰源于混合溶液中的菲。通过异步谱解析出菲的385 nm处荧光峰,证明了异步谱比同步谱具有更好的光谱分辨率。研究结果表明,采用二维荧光相关方法对光谱严重重叠的多组分多环芳烃的解析是可行的,并具有一定的优势,可推广到对环境中其他污染物质的检测。     

Matter-Wave Solitons in Two-Dimensional Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap

We present three families of one-soliton solutions for (2+1)-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.     

Intruder Motion in Two-Dimensional Shaken Granular Beds

The dynamical behavior of an intruder immersed in a two-dimensional shaken granular bed is experimentally investigated. With two types of background particles, f-Г phase diagrams depicting the intruder＇s motion are measured and compared. It is found that even with the same size and density ratio of the intruder to the background particles, the intruder exhibits a distinct behavior at given vibrational conditions： rising behavior in one granular bed; sinking behavior in another granular bed. We slightly tune the size and density ratio to confirm the reliability of the experimental results. In addition, we examine the influences of interstitial air, convection and the initial position on the intruder＇s motion, speculating that the opposite motion could be traced to the material properties of the background particles.     

A Mathematical Representation of Quantizing the Motion of Electrons in a Magnetic Field

It is shown that the concept of a continuous variation in the kinetic energy of a free longitudinal electron motion along the direction of an external magnetic field results in a physically incorrect conclusion on a zero phase volume in the system where the zero Landau lever is realized. Since the kinetic energy of a longitudinal continuous motion is varied in the same way between 0 and 2_B H within each Landau energy level, this problem is circumvented.     

Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q ₁=+1) and negatively (q ₂=–1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) <4. The mapping of the Coulomb gas is made onto the complex Bullough–Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small- expansion and close to the collapse =4 point. The comparison is made with the exactly solvable symmetric version of the model (q ₁=+1,q ₂=–1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.     

Long-Time Behavior for the Two-Dimensional Motion of a Disk in a Viscous Fluid

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier–Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive L ^p ?L ^q decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier–Stokes fluid-rigid disk system.