Interplay of the Staggered and Three-Body Interaction Potentials on the Quantum Phases of a Spin-1 Ultracold Atom in an Optical Lattice

The interplay of the staggered and the three-body interaction potentials on the quantum phases of a spin-1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three-body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet-nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three-body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.     

Multichannel Zero-Range Potentials in the Hyperspherical Theory of Three-Body Dynamics

 The hyperspherical adiabatic representation is reviewed. Both the advantages and disadvantages of this representation are discussed. Zero-range potentials are introduced as one way to circumvent one of the disadvantages. It is shown that such potentials can be used to model complex multiparticle interactions. An application to magnetic tuning of Feshbach resonances shows how complex processes can be modeled in a fairly simple way. Received October 18, 2001; accepted for publication October 24, 2001     

三体heritage混合相互作用和核转动惯量的变化

讨论了在费米子动力学对称模型中大形变区核转动惯量的变化机制.指出在无I1带和基带交叉的情况下,heritage混合本身也可以引起转动惯量的变化,但引起混合的相互作用形式是重要的,引入某种三体相互作用后能很好地解释实验事实.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates （BECs） tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time- varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates (BECs) tunnel-coupled by a double-well potential.A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations,which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.     

Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem

Symplectic algebraic dynamics algorithm （SADA ） for ordinary differential equations is applied to solve numerically the circular restricted three-body problem （CR3BP） in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge~Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term cMculations of the CR3BP.     

Excitation Spectrum and Momentum Distribution of Bose-Hubbard Model with On-site Two-and Three-Body Interaction

An effective action for Bose-Hubbard model with two-and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis.From this effective action,superfluid-Mott insulator(MI) phase transition,excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation.In addition the effects of three-body interaction are also discussed.     

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

Solutions to the general classical Coulomb three-body problem in the form of rigid-rotator and fixed-shape configurations are studied. In the collinear case, some necessary and/or sufficient conditions for the existence of the so-called charge-symmetrical, (−)(+)(−), and charge-asymmetrical, (−)(−)(+), configurations are stated. These conditions involve relations between the geometrical and dynamical parameters of the system under study. The impossibility of the existence of a planar Coulombic rigid rotator is demonstrated. In the two-dimensional case, fixed-shape solutions are studied analytically, and it is shown that, in the three-dimensional case, only fixed-shape solutions involving a triple collision and a static case are possible. Finally, some numerical experimentation, mostly based upon theoretical predictions of the work, is performed, and new bound (although unstable) rotating-oscillating orbits for systems such as the positronium negative ion and helium are found. Received February 27, 1996; revised September 2, 1996; accepted for publication October 22, 1996     

Calculation of Interaction Potentials between Spherical and Deformed Nuclei

The interaction potential for spherical-deformed reaction partners is calculated. The shape, separation and orientation dependence of the interaction potential and fusion cross section of the system ^32S＋^154Sm are investigated within the double-folding model of the deformed nuclei. The effective nucleon-nucleon interaction is taken to be the M3Y-Reid potential. The density is considered for three terms of the expansion using the truncated multipole expansion method, which is a deformed Fermi shape With quadrupole and hexadecapole for the density distribution of ^154Sm. It is found for the interaction potential that the height and the position of barrier strongly depend on the deformations, the orientation angle of the deformed nucleus, and hence produce great effects on fusion cross section. The integrated fusion cross section is in good agreement with the experimental data.     

Mapping of Shape Invariant Potentials by the Point Canonical Transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the Pöschl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulthén potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for Pöschl-Teller type I and Hulthén is SU(2).     

Quark Contribution to the Nucleon Polarizabilities and Three-Body Forces

 Lower and upper bounds to the electric polarizability and para-magnetic susceptibility are explicitly calculated by means of a sum-rule technique and within a large variety of constituent quark models. The role of three-body forces in the potential model is investigated in detail as well as the effects of SU(6) breaking terms. The quark degrees of freedom give a quite sizeable contribution to the static polarizability and the meson cloud accounts roughly for 30% and 60% of the electric proton and neutron polarizability respectively. The quark contribution to the paramagnetic susceptibility is even higher and the mesonic effects are rather uncertain. Received July 28, 1998; revised February 19, 1999; accepted for publication March 4, 1999     

ATOMKI-ECRIS由离子源向等离子体装置的改造

In order to extend the capabilities of the ATOMKI-ECRIS it is being transformed into a modified plasma device by changing its three main components with new ones.The cylindrical plasma chamber is replaced by a larger one(ID=10cm,L=40cm).A new NdFeB multi-pole radial trap was designed and purchased.The basic configuration is 6-pole,but 8-or 12-pole arrangements can also be formed later.The Dresent microwave source(2000W,14.5GHz)and two additional low-power,wide frequency TWT amplifiers give many opportunities to form plasmas with different sizes and characters. Actually a new facility with two sharply different operation modes is being established.All the modifications are reversible so the transformation of the ECRIS into this new device or back can be easily done.     

Effect of Surface Potentials on Interaction between Ions and Surfaces

It is shown by studying the scattering of helium and neon ions with hyperthermal energies on the surfaces of semiconductors that the crystal surfaces reflect some incident ions by means of pairwise interaction and some ions with no loss of energy. Reflection without loss of energy is also assumed to occur due to pairwise interaction between ions and surface atoms bound to underlying atoms by a rigid interaction potential.     

Interaction of Double Sine-Gordon Solitons with External Potentials:an Analytical Model

Interaction of double sine-Gordon solitons with a space dependent potential wall as well as a potential well is investigated by employing an analytical model based on the collective coordinate approach.The potential is added to the model through a suitable nontrivial metric for the background spacetime.The model is able to predict most of the features of the soliton-potential interaction.It is shown that a soliton can pass through a potential barrier if its velocity is larger than a critical velocity which is a function of the initial soliton conditions and also characters of the potential.It is interesting that the solitons of the double sine-Gordon model can be trapped by a potential barrier and oscillate there.This situation is very important in applied physics.The soliton-well system is investigated by using the presented model.Analytical results are also compared with the results of the direct numerical solutions.     

Total Pairwise Quantum Correlation and Entanglement in a Mixed-Three-Spin Ising-XY Model with Added Dzyaloshinskii-Moriya Interaction under Decoherence

We investigate the behavior of geometric global quantum discord(GGQD) and concurrence(C) between halfspins of a mixed-three-spin(1/2,1,1/2) system with the Ising-XY model for which spins(1,1/2) have the Ising interaction and half-spins(1/2,1/2) have both XY and the Dzyaloshinskii-Moriya interactions together,under the decoherence action.A single-ion anisotropy property with coefficient ζ is assumed for the spin-integer.This system which includes an analytical Hamiltonian is considered at the front of an external homogeneous magnetic field B in thermal equilibrium.Finally,we compare GGQD and C and express some interesting phase flip reactions of the total quantum correlation and pairwise entanglement between spins(1/2,1/2).Generally,we conclude that the concurrence and GGQD have different behaviors under the phase Hip channel.     

The c-Term of the Tucson-Melbourne Three-Body Force: To Be or Not to Be

 By Faddeev calculations of ³H we study the dependence of the binding energy on the three-nucleon force. We adopt the 2π-exchange Tucson-Melbourne three-nucleon force and investigate phenomenologically the dependence on the strength of the individual three-body force operators (the a-, b-, c-, and d-terms). While it is well known that the a-term is not as important as the b- and d-terms to gain the experimental binding energy, we find two solutions for the c-term, one around the value used in the original Tucson-Melbourne model and a new one close to zero. A tensor-analyzing power T ₂₀ of the pd elastic scattering using the modified Tucson-Melbourne model, which follows the recommendation by chiral perturbation theory that the short-range c-term should be dropped, describes the data well. Received April 22, 1999; revised June 6, 2000; accepted for publication June 16, 2000     

碱土金属原子与Ne原子间相互作用势的理论计算

本文基于无任何可调参数的势模型计算了碱土金属原子(Be、Mg、Ca、Sr、Ba)与Ne原子间相互作用势,得到的势能曲线及势阱位置和深度与现有的从头计算结果符合较好.本文的计算结果进一步验证了碱土金属原子与稀有气体原子间交换能主要来自碱土金属原子最外层s电子与稀有气体原子最外层p电子之间的交换作用.