非线性三能级体系的绝热朗道-齐纳隧穿

研究了绝热条件下非线性三能级体系的朗道-齐纳隧穿.通过研究体系的本征值和本征态，发现当非线性不是很强时，三个能级的结构与线性情况相似，但中间能级所对应本征态的性质分段，这种分段导致绝热定理被破坏，引起所谓的绝热隧穿现象.由于本征态的不稳定性，造成隧穿率的混乱.当非线性较强时，能级结构发生非常复杂的扭曲，使绝热定理被更加严重地破坏.还讨论了这个模型在三势阱波色-爱因斯坦凝聚体系中的可能应用. 关键词： 三能级 朗道-齐纳隧穿 隧穿率     

Energy spectrum and entanglement of two tunnel- coupled Bose--Einstein condensates

This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose--Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.     

Exact results for the spectra of bosons and fermions with contact interaction

An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. The FQHE N-fermion model with Laplacian-delta interactions is also considered along the same lines of analysis. New exact eigenstates are proposed, along with the Slater determinant, whose eigenvalues are shown to be related to Catalan numbers.     

A New Method to Study Hawking Radiation of Charged Particle from Stationary Axisymmetric Sen Black Hole

Taking the self-gravitation interaction and energy conservation,charge conservation and angular momentum conservation into accpunt, we discuss the tunnelling characteristics of the charged particle from Sen black hole by the Hamilton-Jacobi method. The result shows that the tunnelling probability is related to the change of Bekenstein-Hawking entropy, and the actual radiation spectrum deviates from the pure thermal one, which is consistent with the result of Parikh and Wilczek and gives a new method to correct the Hawking pure thermal spectrum of Sen black hole.     

非线性朗道-基纳隧穿

介绍一种新的量子隧穿———非线性朗道-基纳隧穿.这种隧穿一般发生在有相互作用的二能级系统中,比如光晶格中的玻色-爱因斯坦凝聚物和分子磁体.相对于传统的线性朗道-基纳隧穿,非线性朗道-基纳隧穿由排斥相互作用带来的非线性会增强隧穿的概率.特别是当非线性非常强时,系统的绝热性会遭到破坏;一个无穷小的线性驱动都会造成有限的隧穿概率.     

The eigenstates and tunnelling time in an interdiffused AlGaAs/GaAs quantum well by the transfer matrix method

A matrix method has been used for the determination of the confined eigenstates and their corresponding tunnelling times in an interdiffused AlGaAs/GaAs single quantum well structure. The nonlinear confinement potential profile of the disordered quantum well is due to the interdiffusion of the constituent Al and Ga atoms and is modeled here by an error function. The results indicate that the interdiffusion, as well as the applied electric field, affect the tunnelling times and the energy linewidths of the corresponding states. The results are compared with those for an AlGaAs/GaAs as-grown single square quantum well without any interdiffusion.     

Three-body interaction and phonon dispersion relations in aluminium

Based on an ab initio cohesive energy calculation and a model of three-body interaction, the pair potential can be calculated using the Möbius inversion theorem in the theory of numbers. Then the atomic force constants and the phonon dispersion for A1 are evaluated both with and without three-body interaction. Compared with experiments, the results show that taking the three-body interaction into account considerably improves the dispersions. Contrary to previous work, the method for calculating the atomic force constants and phonon dispersions presented here is simple, with only two adjustable parameters.     

Effects of three-body interactions on the dynamics of entanglement in spin chains

With the consideration of three-body interaction, dynamics of pairwise entanglement in spin chains is studied. The dependence of pairwise entanglement dynamics on the type of coupling, and distance between the spins is analyzed in a finite chain for different initial states. It is found that, for an Ising chain, three-body interactions are not in favor of preparing entanglement between the nearest neighbor spins, while three-body interactions are favorable for creating entanglement between remote spins from a separable initial state. For an isotropic Heisenberg chain, the pairwise concurrence will decrease when three-body interactions are considered both for a separable initial state and for a maximally entangled initial state, however, three-body interactions will retard the decay of the concurrence in an Ising chain when the initial state takes the maximally entangled state.     

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.     

Tunnelling through randomly inhomogeneous barriers as a special problem of the scattering theory

The tunnelling of electrons through an inhomogeneous delta barrier is considered. The strength of the barrier is defined as a function oscillating around a constant mean value along a plane. Owing to deviations from this value, the tunnelling through such a delta barrier has to be interpreted as a scattering. A simple model is discussed when circular windows of a given radius b representing themselves delta barriers of a given strength γ₀ are embedded in a homogeneous delta barrier defined with another strength . When the centers of the windows are distributed randomly in the barrier plane, the potential energy of the electrons is a random function of two space coordinates. The perpendicular incidence is discussed with emphasis on the angular probability density of the tunnelled electrons. The derivation of the angular probability density proves that three basic quantum-mechanical phenomena can be described by one simple formula: tunnelling, diffraction and scattering.     

Study of high-pressure phase transition of CeTe and EuTe through three-body interaction potential approach

The high pressure phase transition of lanthanum monotellurides having NaCl-type (B₁) structure have been studied using three-body interaction potential (TBIP) approach. The potential model consists of long-range Coulombic, three-body interaction forces, short-range overlap repulsive forces operative up to next nearest neighbor ions, van der Walls interactions and zero point energy effects. To understand the effect of pressure on elastic constant and their combinations, they have also been studied. The Born stability criterion was also found to be fulfiled in the present study. Our calculated results of phase transitions, volume collapses and elastic behavior of these monotellurides are found to be close to the experimental results. This shows that the inclusion of three-body interaction effects makes the present model suitable for high-pressure studies.     

Coherent Tunnelling in Coupled Quantum Wells under a Uniform Magnetic Field

Coherent tunnelling is studied in the framework of the effective mass approximation for an asymmetric coupled quantum well. The Hartree potential due to the electron-electron interaction is considered in our calculation. The effects of the longitudinal and transverse magnetic field on coherent tunnelling characteristics are discussed. It has been found that the external field plays an important role in modulating the electron states.     

Generation of Bell states in two-component Bose－Einstein condensates

We examine analytically the generation of Bell state in Bose condensates of two interacting species trapped in a double well configuration. The density of probability for finding the entangled Bell state is given. The effect of the tunnelling rate and the interspecies interaction strength on the generation of Bell state is discussed. We find that the oscillation amplitude of the density of probability for finding the entangled Bell state becomes greater as the tunnelling rate Ω increases, and the self-interaction strength of the component A(B) has no effect on it.     

Dynamics of entanglement in one-dimensional Ising chains with two- and three-body interactions

The evolution of entanglement in a one-dimensional Ising chain with both two-body and three-body interactions, under two types of initial states, is numerically simulated. We analyse three problems concerning the dynamics of pairwise entanglement: (i) the possibility of generating large entanglement from an initial separable state by the use of a selective irradiation scheme; (ii) the effect of three-body interaction on the generation of entanglement from an initial separable state; (iii) the effect of three-body interaction on the decay of the entanglement from a state with only (m,n)-pair maximal entangled, and the rest in product form. It is shown that a large pairwise concurrence C_mn can be obtained when the resonant, transverse radio-frequency fields are selectively switched on from the mth to nth spins. Three-body interaction will decrease the oscillation amplitude of the nearest neighbour concurrence, while the oscillation amplitude of remote pairwise concurrence will be greatly increased with the consideration of three-body interactions. For an initial (m,n)-pair maximal entangled state, a slow decay of the pairwise concurrence C_mn is found with the introduction of three-body interactions.     

隧道电离产生的高次谐波

用隧道电离模型，研究了激光和气体相互作用中，不同气体密度及激光强度下，气体电离及激光能量损耗物过程，并研究了这种效应引起的高次谐波。     

Resonant invisibility with finite range interacting fermions

We study the eigenstates of two opposite spin fermions on a one-dimensional lattice with finite range interaction. The eigenstates are projected onto the set of Fock eigenstates of the noninteracting case. We find antiresonances for symmetric eigenstates, which eliminate the interaction between two symmetric Fock states when satisfying a corresponding selection rule.     

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

We investigate electronic transport through a parallel double quantum dot （DQD） system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit （2e^2/h） due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.     

High-pressure equation of state for solid krypton from interatomic potentials

The pressure-volume isotherm for krypton at 300 K is evaluated by the Monte Carlo method using pair and three-body potentials. The pair potentials used are that of Aziz and Slaman and a slightly modified version of their potential which gives better agreement with high-energy scattering data. The three-body potentials considered are the Axilrod-Teller interaction and the first-order three-body exchange interaction as parametrized by Loubeyre. The results are compared with recent measurements at pressures up to 300 kbar and the implications of the comparison are discussed. The best agreement with experiment is found using the Axilrod-Teller interaction as the only many-body interaction, indicating that the three-body exchange interaction is to a large extent canceled by higher many-body interactions, at least in the highly symmetrical environment of the crystal.This paper is dedicted to Howard Reiss on the occasion of his 66th birthday.     

计及两体和三体作用下的二维凝聚体中的孤子特性

使用多重尺度法,解析地研究计及粒子间两体和三体同时作用下二维凝聚体中孤子的特性. 结果发现,当凝聚体粒子间两体作用为排斥、三体作用为吸引时,凝聚体内会产生暗孤子环,且随着三体吸引作用的减弱,暗孤子环中心峰的高度逐渐降低,并当三体吸引作用消失时暗孤子环演化为一个完美的二维暗孤子. 当两体和三体作用均为排斥时,凝聚体中的暗孤子的宽度和幅度随着三体排斥作用的加强而减小,且当三体作用强度增加到与两体作用同一数量级时,凝聚体产生坍塌现象. 关键词： 玻色-爱因斯坦凝聚体 两体和三体作用 暗孤子     

Ground and Low-Lying Collective States of Rotating Three-Boson System

The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime.The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0 ≤ L ≤ 4N to obtain the ground and low-lying eigenstates.Our numerical results show that breathing modes with N-body eigenenergy spacing of 2hω⊥,known to exist in strictly 2D system with zero-range(δ-function) interaction potential,may as well exist in quasi-2D system with finite-range Gaussian interaction potential.To gain an insight into the many-body states,the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates.In the rapidly rotating regime the ground state in angular momentum subspaces L=(q/2)N(N-1) with q=2,4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose–Laughlin like state.We further observe that the first breathing mode exhibits features similar to the Bose–Laughlin state in having eigenenergy,von Neumann entropy and internal structure independent of interaction for the three-boson system considered here.On the contrary,for eigenstates lying between the Bose–Laughlin like ground state and the first breathing mode,values of eigenenergy,von Neumann entropy and internal structure are found to vary with interaction.