Magnetic field effect on state energies and transition frequency of a strong-coupling polaron in an anisotropic quantum dot

By employing a variational method of the Pekar-type, which has different variational parameters in the x–y plane and the z-direction, we study the ground and the first excited state energies and transition frequency between the ground and the first excited states of a strong-coupling polaron in an anisotropic quantum dot (AQD) under an applied magnetic field along the z-direction. The effects of the magnetic field and the electron–phonon coupling strength are taken into account. It is found that the ground and the first excited state energies and the transition frequency are increasing functions of the external applied magnetic field. The ground state and the first excited state energies are decreasing functions, whereas transition frequency is an increasing function of the electron–phonon coupling strength. We find two ways of tuning the state energies and the transition frequency: by adjusting (1) the magnetic field and (2) the electron–phonon coupling strength.     

基于Gross-Pitaevskii能量泛函求解谐振势阱中玻色凝聚气体基态波函数

基于Gross-Pitaevskii(G-P)平均场能量泛函和变分方法，对囚禁在谐振势阱中的玻色凝聚气体，在T=0K时的基态波函数提出一种新解法.运用这一方法能得到基态波函数的解析表达式，求解出系统的化学势与凝聚原子数的关系等.其结果与Edwards和Dalfovo等人直接数值求解G-P方程所得到的结果相一致，并在Na_s/a1大原子数N的极限条件下，与托马斯-费米近似模型的结论也趋向一致.该方法计算简单，而且能够进行解析处理. 关键词： 玻色凝聚气体 G-P泛函 谐振势阱 基态波函数     

Improvement of variational approach in an interacting two-fermion system

A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a one-dimensional(1D) harmonic potential. At the boundaries both the wave function and its first derivative are continuous and the quasi-momentum is determined by a more practical constraint condition which associates two variational parameters. The upper bound of the ground state energy is obtained by applying the variational principle to the expectation value of the Hamiltonian of relative motion on the trial wave function. The resulted energy and wave function show better agreement with the analytical solution than the original proposal.     

磁场对石墨烯中弱耦合极化子性质的影响

研究了磁场作用下石墨烯中电子与表面光学声子弱耦合情况下的极化子的性质。采用线性组合算符和Pekar变分法分别推导出了石墨烯中弱耦合极化子的基态能量E₀、第一激发态能量E₁和跃迁频率ω随磁场强度B和德拜截止波数k_d之间的变化关系。数值计算结果表明,极化子的基态能量E₀随磁场强度B变化的曲线（k_d一定时）和E₀随k_d的变化曲线（B一定时）均会分裂成对称的两条,并且当B一定时E₀的绝对值随k_d的增加而增加。在k_d一定时,极化子的第一激发态能量E₁和跃迁频率ω均为磁场B的增函数;在B一定时,E₁和ω均随k_d的增加而增大。     

Phase transitions in a few-electron quantum dot in a magnetic field: Wigner phases and broken-symmetry spin-singlet states

We develop a variational many-body approach within a second quantized formulation for a few-electron system in a parabolic two-dimensional quantum dot (QD). By way of application, the nature of the ground state of a two-electron system in a parabolic QD in a broad range of magnetic fields is theoretically investigated. Various phase transitions on the basis of the resulting analytical expressions for energy of the system have been investigated: First, the well-known transition from a maximum density droplet to a Wigner phase in a magnetic field is obtained, provided that the QD is in conditions of weak confinement. Furthermore, in the case of relatively strong QD confinement and weak magnetic fields, a rotationally symmetric spin-singlet state is the ground state of the system. However, in a strong magnetic field and for the same QD confinement, a broken-symmetry spin-singlet state appears to be energetically favored over the symmetric spin-singlet state. A first investigation of such a broken-symmetry spin-singlet phase in a QD in a magnetic field is shown to be an important application of the proposed technique. The text was submitted by the authors in English.     

耦合强度和磁场对极化子基态的影响

利用线性组合算符和幺正变换相结合的方法,推导出极化子基态与耦合强度和磁场强度的关系。数值计算表明:当磁场强度给定时,随着耦合常数α的增加,振动频率λ先减小后增大;基态能量E₀单调下降;自陷能E_0tr单调增大;Landau能E_0L先增大,达到最大值后又下降。当耦合强度给定时,随着磁场强度的增大,λ单调增大,且α愈小,λ增加愈快;基态能量E₀随磁场强度的增大而增大;自陷能E_0tr随着磁场强度的增大而略有增加;Landau能E_0L随着磁场强度的增大先增大,达到最大值后,又开始下降。     

Interaction effects on persistent current of ballistic cylindrical nanostructures

We investigate clean cylindrical nanostructures with an applied longitudinal static magnetic field. The ground state of these systems becomes degenerate for particular values of the field due to Aharonov-Bohm effect. The Coulomb interaction introduces couplings between the electronic configurations. Consequently, depending on particular selection rules, the ground state may become, in the interacting case, a many body state at the degeneracy points: a gap is then opened. To study this problem, we propose a variational multireference wave function which goes beyond the Hartree-Fock approximation. Using this ansatz, in addition to the replacements of some crossings by avoided crossings, two other important effects of the electron-electron interaction are pointed out: (i) the long-range part of the Coulomb potential tends to shift the position in magnetic field of the crossing or avoided crossing points and, (ii) at the points of degeneracy or near degeneracy, the interaction can drive the system from a singlet to a triplet state inducing new real crossing points in the ground state energy curve as function of the field. In any case, the crossing points that are due to either orbital or spin effects, should manifest themselves in various experiments as sudden changes in the response of the system (magnetoconductance, magnetopolarisability, ...) when the magnetic field is tuned.     

Magnetic field effect on the binding energy of a hydrogenic impurity in coaxial GaAs/ AlxGa1−xAs quantum well wires

We propose a coaxial cylindrical quantum well wire (QWW) system, in which two conducting cylindrical layers are separated by an insulating layer. The ground state binding energy of a hydrogenic impurity subjected to uniform magnetic field applied parallel to the wire axis is studied within a variational scheme as a function of the inner barrier thickness for two different impurity positions and various barrier potentials. The ground state energy and wave function in the presence of a magnetic field is directly calculated using the fourth-order Runge–Kutta method. It is found that the binding energy in critical barrier thickness shows a sharp increase or decrease depending on the impurity position and magnetic field strength. The main result is that a sharp variation in the binding energy, which may be important in device applications, depends strongly not only on the location of the impurity but also on the magnetic field and the geometry of the wire.     

Recent progress in simulation of the ground state of many Boson systems

We present two recent advances in the simulation of ⁴He in the condensed phase at zero temperature. Within the variational theory of strongly interacting bosons we have studied a cluster of ⁴He atoms with one alkali ion K⁺. For the wave function we have used a new shadow wave function (SWF) in which the coupling between one ⁴He atom and its shadow variable depends on its distance from the ion. This substantially improves the energy. The first shell around the ion contains 14 atoms which are spatially ordered. However the atoms of the first shell are not completely localized and frequent exchanges with atoms which are further from the ion take place. This also suggests that at least for the ion K⁺ the atoms of the first shell participate in the superfluidity. We have also introduced a new extension of the path integral ground state (PIGS) method which is able to compute exact ground state expectation values without extrapolations and with a SWF as the trial variational wave function to project on the ground state. This is an important extension which opens up the possibility of studying disorder phenomena in the solid phase by an exact method at zero temperature. We have applied this technique to compute the energy of formation of a vacancy at different densities in the solid phase of ⁴He. This computation confirms the variational result that a vacancy is a delocalized defect in the low density helium solid.     

表面磁极化子的光学声子平均数

采用Tokuda改进的线性组合算符、Lagrange乘子和变分法,讨论了强、弱耦合表面磁极化子的性质。计算了极化子的基态能量和光学声子平均数。以AgCl和ZnS晶体为例进行了数值计算。讨论了表面磁极化子振 动频率、基态能量和光学声子平均数与磁场B和拉格朗日乘子u的关系。     

Resonating valence bond wave functions for strongly frustrated spin systems

The resonating-valence-bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough "quantum frustration." This scenario, proposed a long time ago but never confirmed by microscopic calculations, is strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the J(1)-J(2) Heisenberg model for 0.4 less than approximately J(2)/J(1) less than approximately 0.5. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.     

Properties of One Oxygen Hole Motion in a Quantum Antiferromagnet

By making use of the equation of motion of the Green's function method and the selfconsistent nondiagonal Fock approximation technique, we present a systematic analysis of the ground state properties of one-hole doping in the cupric oxides for the two-band model. The quant urn Bogoliu bov-de Gennes formalism is developed to study the renormalized hole motion with the effects of local distortion of spin configurations. The ground state wave function, the ground state energy and the effective mass are derived. The calculations are carried out with the variational approach.     

Calculation of Binding Energies of the Ground and Excited States of a Donor in Quantum Wells: A Functional Variational Approach

The calculations of the ground and a few low-lying excited states of impurity in the quantum wells (QW's) are presented by making use of a functional variational approach. A new trial wave function is proposed. It is taken by the product of the exact subband state in the Q W and the state of two-dimensional (2D) hydrogenic-like donor with an effective charge distribution along the z-direction (perpendicular to the well interfaces). The variation of binding energies of the donor states in the QW with the well-width is calculated. The calculated result is compared with that obtained by the earlier variational method. The functional variational approach proposed here has some benefits such as, to bring a great flexibility and to apply to a relatively large species of trial wave functions.     

Spatial correlation of two particles in semiconductor quantum ring

We analyze the effect of the spatial correlation on the ground state energy of two particles (two electrons and exciton–hole pair) confined in quantum ring (QR) with a soft-edge-barrier confinement potential. Starting from the Schrödinger variational principle we derive a one-dimensional differential equation for the spatial pair correlation function (SPCF), which we solve numerically by using the shooting method. The effect of the repulsive core in a self-assembled GaAs/InAs QR on the two-electron and exciton SPCF is analyzed. A comparative analysis of the dependencies of the two-particle ground state energies on the inner and outer radii of GaAs/InAs QRs with different confinement potential shapes is presented.     

抛物量子点中强耦合磁极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合磁极化子的基态和激发态的性质。计算了基态和激发态磁极化子的束缚能以及磁极化子的共振频率。讨论了这些量对回旋频率和有效限制强度的依赖关系,以及磁极化子光学声子平均数的性质,结果表明:由于Zeeman劈裂,抛物量子点中磁极化子的回旋共振频率劈裂为两支。基态和激发态磁极化子的束缚能以及磁极化子的共振频率都随回旋频率的增加而增大,随量子点的有效束缚强度的增大而减小。     

A hydrodynamic model for diamagnetic induced currents in molecules

The current set up when a single bound electron moves in a magnetic field obeys simple hydrodynamic equations, which arise from a variational principle. When the ground state is not degenerate they have a unique solution, determined by the unperturbed electron density. The theory is closely related to Wick's irrotational flow model for the currents in a rotating molecule, to Tillieu and Guy's variational method, and London and Rebane's ideas of gauge invariance. Difficulties arise when there is more than one electron, when the wave function has nodes, or when it is degenerate; but the method may be useful for calculating magnetic properties of some small molecules.     

四参数法计算氦原子基态能级研究

在求解氦原子径向Schr dinger方程时,设计了含有四参数的基态波函数,推导出含有四参数的氦原子基态能级表达式,分别采用Matlab 7.0最优化运算和Monte-Carlo法,计算了氦原子的基态能量,得到了相应的波函数.将计算结果与其它文献采用变分法所得计算值及实验值进行了比较,结果表明:这种方法不仅计算简便有效,准确性较高,而且所得氦原子基态空间波函数自动满足空间对称性的要求.     

Electron crystallization using localized representation

The character of the ground state of the electron crystal—an electron gas with periodic density and/or spin density is investigated. Calculations for non-magnetic, ferromagnetic and anti-ferromagnetic electron crystals based on the Koster-Kohn variational principle for direct calculation of Wannier functions are presented. The Wannier function is approximated by a symmetrically orthonormalized Gaussian. The orbital exponent of the Gaussian is used as a variational parameter. The effect of the positive background is suitably taken into account. The results of our calculation support Wigner’s prediction of electron crystallization.     

束缚磁极化子的性质

采用线性组合算符和幺正变换方法分别导出弱、强耦合情形下束缚磁极化子的振动频率和基态能量.结果表明库仑场的存在使得磁极化子的基态能量的绝对值变小.     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.