A Secondary Operator Ordering Problem for a Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum pi (i = 1, 2, 3) in usual kinetic energy (1/2μ)∑p2i, and the correct kinetic energy turns out to be (1/2μ) ∑(1/ fi)pifipi, where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field.     

On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k⁰, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k², two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.     

Three-Body Recombination with Two-Channel Contact Interactions

We use a two-channel contact interaction model to describe a system of three identical bosons. The two-channel model quantitatively describes the phenomena of Feshbach resonance in agreement with the phenomenological expression relating scattering length to magnetic detuning. The model also has a finite effective range. We investigate finite range effects in three-body recombination. The simpler one-channel contact interaction model predicts a characteristic geometric scaling of minima in the recombination coefficient as a function of scattering length with scaling parameter 22.7. We show that this factor is reduced when the effective range is included. We compare calculations to experiment.     

Lepton-Lepton Interactions under a Strong Magnetic Field

The cross-section for the reaction e⁺ + e^? → v + v , under a strong magnetic field is calculated. The rate of energy loss is also calculated. These calculations may be of great importance for astrophysical estimations in neutron stars.     

Nonlinear Landau--Zener Tunnelling with Two and Three-Body Interactions

We investigate the nonlinear Landau-Zener tunnelling of Bose-Einstein condensate （BEC） in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both anaJytically and numerically. The analytical eigenstates and the tunnelling probability are obtained, which are verified by numerical methods. It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.     

Solution of a Relativistic Three-Body Problem

 Starting from a relativistic s -wave scattering-length model for the two-particle input we construct an unambiguous, unitary solution of the relativistic three-body problem given only the masses m _a , m _b , m _c ,and the masses of the two-body bound states μ _bc ,μ _ca ,μ _bc . Received August 5, 1997; revised June 21, 1999; accepted for publication July 10, 1999     

High-Energy Two-Electron Photoabsorption as a Three-Body Problem

We study the high-energy behaviour of double photoionization and of the ionization accompanied by excitation of the states n¹S and n³S of the H^– ion, helium atom, and light helium-like ions. We show that the high-energy nonrelativistic limit of the ionization+excitation to the single-ionization cross section ratio is still valid for the photon energies, corresponding to the relativistic energies of the outgoing electron. The same applies to the double photoionization of the triplet states. The situation for the double photoionization of singlet states differs due to the quasifree mechanism. All these ionization ratios are calculated by using the high-precision locally correct wave functions for the bound electrons. The importance of using locally correct functions is emphasized.     

具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化

运用变分法研究了具有三体作用的玻色-爱因斯坦凝聚暗孤子的演化特性,分析了调谐囚禁电势对暗孤子运动的影响.结果表明,囚禁在调谐势阱中的暗孤子将振动,势阱强度和三体作用的符号影响了暗孤子的演化,并改变了BEC系统的振动特性.     

Coherence of Disordered Bosonic Gas with Two-and Three-Body Interactions

We theoretically and numerically investigate the coherence of disordered bosonic gas with effective two-and three-body interactions within a two-site Bose-Hubbard model.By properly adjusting the two-and three-body interactions and the disorder,the coherence of the system exhibits new and interesting phenomena,including the resonance character of coherence against the disorder in the purely two-or three-body interactions system.More interestingly,the disorder and three-body interactions together can suppress the coherence of the purely three-body interactions system,which is different from the case in which the disorder and two-body interactions together can enhance the coherence in certain values of two-body interaction.Furthermore,when two-or threebody interactions are attractive or repulsive,the phase coherence exhibits completely different phenomena.In particular,if two-or three-body interactions are attractive,the coherence of the system can be significantly enhanced in certain regions.Correspondingly,the phase coherence of the system is strongly related to the effective interaction energy.The results provide a possible way for studying the coherence of bosonic gas with multi-atoms' interactions in the presence of the disorder.     

Duality in the Azbel-Hofstadter Problem and Two-Dimensional d-Wave Superconductivity with a Magnetic Field

A single-parameter family of the lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter h = Delta/t (quantum parameter). A topological number is attached to each energy band. A duality between the classical limit ( h = +0) and the quantum limit ( h = 1) is revealed in the energy spectrum and the topological number. The model has a close relation to two-dimensional d-wave superconductivity with a magnetic field. Making use of the duality and a topological argument, we shed light on how quasiparticles with a magnetic field behave, especially in the quantum limit.     

On a Three-Body Problem in Relativistic Quantum Mechanics

Proceeding from the method of packing operators developed by Sokolov and from the “light front variables” technique, the explicit formulae for packing operators and auxiliary mass operators for a system of three particles with arbitrary spins are derived. It is shown that for the packing operators there exists an infinite number of solutions yielding different physical consequences. The problem of the theory substantiation is discussed; the arguments in favour of a certain choice of packing operators are produced.     

Coherent Destruction of Tunneling of Bosons with Effective Three-Body Interactions

The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically.In our findings,when the system is with only repulsive twobody interactions or only three-body interactions,the tunneling will be suppressed;while in the case of the coupling between two- and three-body interactions,the tunneling can be either suppressed or enhanced.Particularly,when attractive three-body interactions are twice large as repulsive two-body interactions,CDT occurs at isolated points of driving force,which is similar to the linear case.Considering different interaction,the system can experience different transformation from coherent tunneling to coherent destruction of tunneling(CDT).The quasi-energy of the system as the function of the periodically driving force shows a triangular structure,which provides a deep insight into the tunneling dynamics of the system.     

Aspects of Magnetic Field Configurations in Planar Nonlinear Electrodynamics

In the framework of three-dimensional Born-Infeld Electrodynamics, we pursue an investigation of the consequences of the space-time dimensionality on the existence of magnetostatic fields generated by electric charges at rest in an inertial frame, which are present in its four-dimensional version. Our analysis reveals interesting features of the model. In fact, a magnetostatic field associated with an electric charge at rest does not appear in this case. Interestingly, the addition of the topological term (Chern-Simons) to Born-Infeld Electrodynamics yields the appearance of the magnetostatic field. We also contemplate the fields associated to the would-be-magnetic monopole in three dimensions.     

Wave Trains Generation in a Delayed Nonlinear Response of Bose-Einstein Condensates with Three-Body Interactions

We investigate the modulational instability of matter-wave condensates in a modified Gross-Pitaevskii equation which takes into account effects of the three-body interaction. This three-body interaction consists of a quintic term and an additional one representing the delayed nonlinear response of condensates which are trapped both in an attractive and a repulsive harmonic potentials. Our theoretical study uses a modified lens-type transformation and we obtain a modulational instability criterion, and an explicit growth rate. We show that the presence of the three-body interaction destabilizes the condensate, and enhances the appearance of instability in the condensate. Numerical experiments agree well with analytical predictions. Furthermore, our numerical simulations show that the three-body interaction modifies the symmetry of the trail of soliton chains created. The expulsive potential enhances the instability, while the attractive potential appears to soften the instability.     

高温高密度条件下氮分子三体关联效应与冲击压缩特性

 基于量子化学从头计算方法,计算了处于高密度条件下氮分子之间的两体排斥势和三体关联势,并采用球面平均近似求得了它们各自的高温平均势能值,得到了包括三体关联效应的等效两体势函数与分子间距的解析关系。借助分子流体微扰变分理论,并考虑van der Waals长程作用,分别采用总平均两体势和总等效两体势,计算了液氮的冲击压缩曲线。计算结果表明,在不需要考虑分子离解的压缩范围内（1～35 GPa）,三体关联效应的贡献使分子间总等效两体势函数比单独两个分子间总平均作用势函数明显软化,与实验Hugoniot数据结果一致。     

Non-integrability of the Anisotropic Stormer Problem and the Isosceles Three-Body Problem

We study the Anisotropic Stormer Problem (ASP) and the Isosceles Three-Body Problem (IP), from the viewpoint of integrability, using Morales-Ramis theory and its generalization. The study of their integrability presents particular interest since they model important physical phenomena. Both problems can be reduced with respect to the S¹ symmetry. Almeida and Stuchi [M.A. Almeida, T.J. Stuchi, Non-integrability of the anisotropic Stormer problem with angular momentum, Physica D 189 (2004) 219-233] proved that the reduced ASP is non-integrable for almost all values of the parameters. In this paper we establish the non-integrability (in the extended Liouville sense) of the remaining cases. The IP is a special case of the three-body problem and it can be considered as a generalization of the Sitnikov problem. Here we prove that the complexified reduced IP does not admit an additional independent meromorphic first integral.     

CHHE-MRT Method and Its Application in Three-Body Problem

Based on "Hybrid Method" by Dzhibuti,a CHHE-MRT method is suggested for threebody problem,which overcomes the difficulty of infinite integral of oscillatory Bassel functions in hybrid method,and enables us to study the bound states and scattering states of three-body problem by using Gauss,Exponential and Yukawa potential.