Relativistic symmetries with the trigonometric Poeschl-Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poeschl-Teller （tPT） potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ（κ± i 1）r^-2. In view of spin and pseudo-spin （p-spin） symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method （AIM）. We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.     

Relativistic symmetries in the Rosen-Morse potential and tensor interaction using the Nikiforov-Uvarov method

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen- Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ(κ± 1)r 2 . In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov-Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.     

Relativistic symmetries in the Hulthn scalar-vector-tensor interactions

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for scalar-vector-tensor Hulthn potentials are obtained with any arbitrary spin-orbit coupling number κ using the Pekeris approximation. The Hulthn tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given.     

Relativistic symmetries in the Hulth6n scalar-vector-tensor interactions

In the presence of spin and pseudospin （p-spin） symmetries, the approximate analytical bound states of the Dirac equation for scalar-vector-tensor Hulth6n potentials are obtained with any arbitrary spin-orbit coupling number using the Pekeris approximation. The Hulth6n tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov-Uvarov （NU） method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given.     

Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric(SUSY) quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrdinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.     

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.     

Spin and pseudospin symmetric Dirac particles in the field of Tietz-Hua potential including Coulomb tensor interaction＊

Approximate analytical solutions of the Dirac equation for Tietz-Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin-orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms κ(κ± 1)r-2 . Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov-Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.     

Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.     

Relativistic symmetry of position-dependent mass particles in a Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

Relativistic Symmetries in the Hulthén-like Potential and Tensor Interaction

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for Hulthén-like potential including a Coulomb-like tensor interaction are obtained with any arbitrary spin–orbit coupling number κ using the Pekeris approximation. The generalized parametric Nikiforov–Uvarov (NU) method is used to obtain the energy eigenvalues and the corresponding wave functions in their closed forms. We show that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.     

Relativistic New Yukawa-Like Potential and Tensor Coupling

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number ${\kappa}$ . In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction, ?T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schr?dinger solutions for Yukawa and inversely quadratic Yukawa potentials.     

Dynamical properties of the Haldane chain with bond disorder

By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the S = 1 antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at δ_∆ ~ 0.5 with more and more low-energy excitations coming out. After the critical disorder strength δ_c ~ 1, the system reaches a random-singlet phase with prominent sharp peak at ω = 0 and broad continuum at ω > 0 of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These “spins” can form the weakly coupled longrange singlets due to quantum fluctuation which contribute to the sharp peak at ω = 0.     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

非马尔科夫环境中各向异性海森堡自旋链的量子失协

利用量子失协方法研究在非马尔科夫环境中具有时变磁场的两比特各向异性海森堡XYZ模型量子失协的动力学演化。海森堡XYZ系统的初始态为最大纠缠态 $\left|\psi_{A B}\right\rangle=(1 / \sqrt{2})(|11\rangle+|00\rangle)$ , 利用非马尔科夫量子态扩散方法解析求解非马尔科夫主方程, 得出系统的约化密度矩阵; 然后代入量子失协公式得出系统量子失协的演化动力学。讨论自旋耦合强度、环境关联系数γ和余弦磁场强度B对量子失协动力学的影响。研究发现: 当环境关联系数γ较小时, 系统的量子失协明显呈现上升趋势, 因此可以表明非马尔科夫环境具有增加系统量子失协的作用。同时较大的自旋耦合系数J和J_Z以及余弦磁场强度B也具有增加系统量子失协的作用。     

准周期层状铁磁超晶格的实空间重整化群方法

本文用实空间重整化群方法讨论了准周期层状铁磁超晶格的磁自旋波,用Reduce语言推导了decimation变换公式,从而求得了局域格林函数、局域态密度和约化磁矩。发现局域态密度的带宽和约化磁矩与最近邻相互作用J₁、J₂及格点自旋s_a、s_b密切相关。     

Proper In deposition amount for on-demand epitaxy of InAs/GaAs single quantum dots

The test-QD in-situ annealing method could surmount the critical nucleation condition of InAs/GaAs single quantum dots(SQDs) to raise the growth repeatability.Here,through many growth tests on rotating substrates,we develop a proper In deposition amount(θ) for SQD growth,according to the measured critical θ for test QD nucleation(θ_c).The proper ratio θ/θ_c,with a large tolerance of the variation of the real substrate temperature(T_(sub)),is 0.964-0.971 at the edge and 0.989 but 0.996 in the center of a 1/4-piece semi-insulating wafer,and around 0.9709 but 0.9714 in the center of a 1/4-piece N~+ wafer as shown in the evolution of QD size and density as θ/θ_c varies.Bright SQDs with spectral lines at 905 nm-935 nm nucleate at the edge and correlate with individual 7 nm-8 nm-height QDs in atomic force microscopy,among dense 1 nm-5 nm-height small QDs with a strong spectral profile around 860 nm-880 nm.The higher T_(sub) in the center forms diluter,taller and uniform QDs,and very dilute SQDs for a proper θ/θ_c:only one 7-nm-height SQD in25 μm~2.On a 2-inch(1 inch = 2.54 cm) semi-insulating wafer,by using θ/θ_c = 0.961,SQDs nucleate in a circle in 22%of the whole area.More SQDs will form in the broad high-T_(sub) region in the center by using a proper θ/θ_c.     

光解苯半醌自由基的CIDEP谱

用高时间分辨ESR谱仪实验给出了光解对苯醌产生的苯半醌自由基的CIDEP发射谱.用三重态机理,同时考虑了自由基对机理的影响,从理论上分析了极化强度,计算出了增强因子V(Ⅰ)=-0.66,V(R)=0.2,一级反应速率k_1,A=0.05/μs,二级反应速率β=0.02/μs,横向和纵向弛豫时间T₁≈T₂=2.3μs.