磁场对异质界面上D-中心的影响

势阱中的类氢杂质的能级问题一直为学术界所长期关注。讨论了异质界面上中性施主D⁰和负施主离子D^-的能量随垂直于界面的磁场的变化情况,同时将磁场和势阱结合起来考虑其对类氢杂质的影响。研究发现随磁场的增大,其对D⁰基态能的影响越来越大,对其束缚能的影响逐渐变小,而对D^-中心,磁场的作用使得D^-由非束缚态转变为束缚态。计算中分别选取了两种不同的波函数,分析了这两种波函数的适用范围,利用变分的方法得到此结构中D⁰中心的基态能量和束缚能与D^-中心角动量L=-1自旋三重态的本征能量和束缚能随磁场的变化关系,找到了此三重态由非束缚态转变到束缚态对应磁场的阈值。     

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseu- dospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.     

A spatial finite size scaling method for calculation of critical parameters for weakly bound states

We present a finite size scaling approach to calculate critical parameters and exponents of quantum few-body system for which a bound state energy becomes absorbed or degenerates with the continuum. The scaling is done by introducing a cutoff radius for the potential. The asymptotic behavior for large values of the cutoff parameter is determined by the exact critical parameters.     

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.     

Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.     

Single parameter scaling in one-dimensional localization revisited

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned delta functions with random strength.     

A negatively charged exciton in a quantum disc

The properties of the bound states of the negatively charged exciton X⁻ in a quantum disc with a confined parabolic potential are studied using exact diagonalization techniques. The binding energy spectra of the ground state and the first excited state are calculated as a function of the confinement strength and the effective electron-to-hole mass ratio. The results we have obtained show that the binding energies are closely correlated to the strength of the confinement potential and the effective electron-to-hole mass ratio.     

A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential

In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.     

Bound states and resonant states of three self-gravitating Bose-Einstein condensates

The effect of Yukawa potentials on the bound states and resonance states for systems with three self-gravitating bosons and fermions has been investigated using highly correlated basis functions. The complex coordinate rotation method is used to extract resonance parameters. We have investigated the Borromean binding for such systems. The ground and excited state energies, resonance energy and width for the lowest two resonances are reported for different screening parameters along with the critical range for Borromean binding.     

等离子体效应对碳的类氢离子能级的影响

通过在狄拉克方程中考虑德拜休克尔(Debye-Hückel)屏蔽势,研究了类氢离子C5 低能级能量1s(2S1/2),2s(2S1/2),2p(2P1/2和2P3/2)随等离子体电子温度及电子密度的变化规律,计算得到类氢离子C5 能级能量及能级电离势随等离子体环境的变化关系。同时,拟合得到了基于德拜休克尔屏蔽势下相当好的束缚态能级能量随等离子体环境变化的解析公式,利用该公式得到了类氢离子C5 相应各能级发生压致电离的临界电子密度,其结果与其它文献比有很好的可比性。结果表明:束缚态能级能量随等离子体电子温度的升高而减小,随等离子体电子密度的增大而增大。能级能量百分漂移量的对数值与等离子体电子密度的对数值以及等离子体电子温度的对数值之间均呈现出近似线性关系。对计算等离子体电离态分布及光谱模拟具有一定的意义。     

Resonances in A=6 Nuclei: Use of Supersymmetric Quantum Mechanics

We propose a novel theoretical technique for the calculation of resonances at low excitation energies in weakly bound systems. Starting from an effective potential, supersymmetric quantum mechanics can be successfully used to generate families of isospectral potentials having desirable and adjustable properties. For resonance states, for which there is no bound ground state of the same spin-parity, one can construct an isospectral potential with a bound state in the continuum (BIC). The potential looks quite different but is strictly isospectral with the original one. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family facilitating an easier and more accurate calculation of the resonance energy. Application to ⁶He, ⁶Be, and ⁶Li systems yields quite accurate results. The beauty of our technique: We get both the bound ground state and the resonances by a single technique and using the same potential.     

One Dimensional Models with a Singular Potential of the Type −<Emphasis Type="Italic">αδ</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)+<Emphasis Type="Italic">βδ</Emphasis>′(<Emphasis Type="Italic">x</Emphasis>)

We study a one-dimensional singular potential plus two types of regular interactions: constant electric field and harmonic oscillator. In order to search for the bound state energies, we shall use the Lippman-Schwinger Green function technique. Another direct method will be mentioned for the harmonic oscillator. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy “quasibound states” appear. The harmonic oscillator demonstrates the general result that for a symmetric potential the odd states are not altered whereas the even states energies are lowered or raised accordingly as the delta perturbation is attractive or repulsive. No states are created or annihilated.     

Stochastic heterostructures and diodium in B/N-doped carbon nanotubes

Carbon nanotubes are one dimensional and very narrow. These obvious facts imply that, under doping with boron and nitrogen, microscopic doping inhomogeneity is much more important than for bulk semiconductors. We consider the possibility of exploiting such fluctuations to create interesting devices. Using the self-consistent tight-binding technique, we study heavily doped highly compensated nanotubes, revealing the spontaneous formation of structures resembling chains of random quantum dots, or nanoscale diodelike elements in series. We also consider truly isolated impurities, revealing simple scaling properties of bound state sizes and energies.     

Resonances of Dirac Particle in the Yukawa Potential

We applied the complex scaling method to study the resonances of a Dirac particle in the Yukawa potential, and obtained the corresponding energies and widths. In the non-relativistic limit, our results are in excellent agreement with those by non-relativistic calculations with J-matrix approach. Furthermore, we found that the energies and widths of spin doublets are approximately degenerate, and preserve a good spin symmetry. The quality of spin symmetry is correlated with the parameters of the Yukawa potential.     

Three-particle bound states for partly nonlocal interactions with continuum bound states

We determine the binding energies of the model triton for two partly nonlocal interactions consisting of a local potential with a strong repulsive core and a nonlocal separable interaction acting only inside the core region, which is responsible for the occurrence of a continuum bound state at very high energies in the total interaction. The ground state of the three-particle system does not collapse in this case as for purely nonlocal interactions. The occurrence of a continuum bound state is therefore only a necessary but not a sufficient condition for such an unphysical collapse in few particle systems.     

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.     

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle's energy is less than the potential at both negative and positive infinity. The particle's energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions,which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues,angular momentum numbers,screening parameters,reduced mass,and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.     

On the relation between the hellmann energy functional and the ground state energy of anN-fermion system

The Hellmann energy functional is derived from the Schrödinger variational principle. It is shown to be an upper bound on the ground state energy of anN-fermion system. Its limiting behaviour for small and large particle numbers is discussed.     

Bound state solution of the Klein-Gordon equation for vector and scalar Hellmann plus modified Kratzer potentials

In this study, the analytical solutions of the Klein–Gordon equation for any l states of the scalar and vector Hellmann plus modified Kratzer potential are derived by using an approximation method to the centrifugal potential term. The analytical expressions for eigenvalues and corresponding normalized eigenfunctions of the spin-zero particle have been estimated by using the parametric Nikiforov-Uvarov method. The solution for the radial part of the Klein-Gordon equation is formulated in terms of the generalized Jacobi polynomials. The energy state equation and the wave function for special cases are in good agreement with the previous literature. In addition, we have measured the numerical results of the energy eigenvalues and also the trend of the eigenvalues concerning of different potential parameters have been plotted. Furthermore, it was shown that the energy levels E and quantum numbers n and l are inversely proportional to each other.