含有非谐振势系统能谱的研究

非谐振势V(x)=λx4有着广泛的应用,对其能谱的研究有着重要的意义.采用超对称量子力学和变分法,求解含有非谐振势系统的能谱 关键词： 超对称量子力学 变分法 非谐振势     

包含非中心电耦极矩的环状非谐振子势场赝自旋对称性的三对角化表示

提出了一个包含非中心电耦极矩分量的环状非谐振子势模型,在能够负载Dirac波动算子三对角化表示的完全平方可积L~2空间讨论了这一势场的赝自旋对称性.利用三对角化矩阵方案,使得求解Dirac方程转换为寻求波函数展开系数满足的三项递推关系式.角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示.由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱,显示出这一势模型具有严格的赝自旋对称性     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

超越平均原子模型模拟高温高密等离子体离子布居

从实际应用的角度出发，常采用平均原子(AA)模型进行简化处理.为了能更精确计算高温高密等离子体的离子布居，提出了一套超越AA模型的方法.该方法能够较好地处理局域热动平衡(LTE)等离子体离子布居，也可有效地处理非局域热动平衡(n-LTE)等离子体离子布居. 关键词： 平均原子(AA)模型 离子布居 非局域热动平衡(n-LTE)     

Hulthen势场中Schrdinger方程束缚态问题的超对称量子力学

应用超对称量子力学 (SQM)方法得到了具有Hulthen势的Schr dinger方程能量本征值谱和本征函数的精确解 .分析表明 :Hulthen势是一种形状不变势 ,Hulthen势场中量子力学束缚态的数目是有限的 .     

非理想第二类超导体局域磁弛豫的计算模拟：非均匀钉扎势和表面势垒影响

从热激活模型出发,对非理想第二类超导的局域磁行为进行了计算模拟.讨论了超导体体内非均匀钉扎势和表面势垒对局域磁通运动的影响.计算结果表明,体内非均匀钉扎势对磁通线的运动产生大的阻碍,表面势垒明显抑制了磁通线的进入和离开样品.相对于样品的平均磁弛豫行为和平均磁滞回线,非均匀钉扎以及扫场速率的差异更强地显示在样品的局域磁行为. 关键词： 非理想第二类超导体 局域磁弛豫 非均匀钉扎 表面势叠     

强非局域非线性介质中的涡旋光孤子

满足强非局域条件时，光束在非局域非线性介质的传输过程由Snyder-Mitchell模型描述.在旋转柱坐标系下求解了Snyder-Mitchell模型，得到涡旋光孤子的自相似旋转解析解.结果表明，涡旋光孤子解在径向是惠特克函数与幂函数的乘积，光束的光强呈环形分布，光束绕光束中心旋转. 关键词： 非局域非线性介质 强非局域性 涡旋光孤子 惠特克函数     

环状非有心势场中Schr(o)dinger方程的精确解

提出了一个新的环状非有心势模型.利用Nikiforov-Uvarov方法求解了其满足的Schrodinger方程,得到了束缚态波函数的精确解及能谱方程.讨论了角向分量对径向分量的影响及相关参数取特定值时的特殊情况.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

双环形Coulomb势Schrdinger方程束缚态的精确解(英文)

双环形Coulomb势是指在氢原子势外面再加上一个双环形平方反比势,该模型势是在讨论类似于苯环分子结构的基础上提出的,该模型势在分子和原子物理中有着广泛的应用.本文研究了双环形Coulomb势Schr dinger方程的束缚态精确解,所采用的方法是首先对双环形Coulomb势的Schr dinger方程在球坐标系中进行分离变量,得到相应的角向方程和径向方程;证明双环形Coulomb势在角向和径向具有超对称性和形不变性;根据超对称性和形不变性的性质,获得了角动量量子化条件和束缚态的能谱方程,并将归一化角向波函数用Jacobi多项式表示,将归一化径向波函数用Laguerre多项式函数表示.体系的波函数和束缚态能谱性质由三个量子数n、m和s及势参数,αa和b描述.本文说明量子物理中一些具有对称性的非中心势有精确解,用超对称性和形不变性方法还可以讨论其他形式的非中心势.     

Nonlocal interactions and particle number fluctuations in a solvable model

We present an extension of Bardeen's model for the formation of Cooper pairs that includes a schematic representation of a nonlocal interaction. The model is exactly solvable and we investigate its Hartree-Fock, BCS and Hartree-Fock-Bogoliubov approximations focusing upon the role and significance of the particle number dispersions.     

Exactly solvable two-dimensional stationary Schrödinger operators obtained by the nonlocal Darboux transformation

The Fokker–Planck equation associated with the two-dimensional stationary Schrödinger equation has the conservation law form that yields a pair of potential equations. The special form of Darboux transformation of the potential equations system is considered. As the potential variable is a nonlocal variable for the Schrödinger equation that provides the nonlocal Darboux transformation for the Schrödinger equation. This nonlocal transformation is applied for obtaining of the exactly solvable two-dimensional stationary Schrödinger equations. The examples of exactly solvable two-dimensional stationary Schrödinger operators with smooth potentials decaying at infinity are obtained.     

Modeling of Coulomb interaction in parabolic quantum wires

We study the exciton states in a parabolic quantum wire. An exactly solvable model is introduced for calculating the exciton state and the binding energy as a function of the radius of the quantum wire within the envelope-function approximation. In the calculation, we replace the actual Coulomb interaction between the electron and the hole by a Gaussian nonlocal separable potential and obtain closed expressions for both the envelope-function and the binding energy. Results are compared with those obtained by perturbative methods.     

Nonperturbative gadget for topological quantum codes

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly nonlocal interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. In this Letter, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians nonperturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasiparticle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other nonlocal spin Hamiltonians may be possible.     

The (0,2) exactly solvable structure of chiral rings,Landau-Ginzburg theories and Calabi-Yau manifolds

We identify the exactly solvable theory of the conformal fixed point of (0,2) Calabi-Yau σ-models and their Landau-Ginzburg phases. To this end we consider a number of (0,2) models constructed from a particular (2,2) exactly solvable theory via the method of simple currents. In order to establish the relation between exactly solvable (0,2) vacua of the heterotic string, (0,2) Landau-Ginzburg orbifolds and (0,2) Calabi-Yau manifolds, we compute the Yukawa couplings of the exactly solvable model and compare the results with the product structure of the chiral ring which we extract from the structure of the massless spectrum of the exact theory. We find complete agreement between the two up to a finite number of renormalizations. For a particularly simple example we furthermore derive the generating ideal of the chiral ring from a (0,2) linear σ-model which has both a Landau-Ginzburg and a (0,2) Calabi-Yau phase.     

Light scattering by a finite obstacle and fano resonances

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering. An exactly solvable one-dimentional discrete model with nonlocal coupling for simulating diffraction in wave scattering in systems with reduced spatial dimensionality is also introduced and analyzed. Deep connections between the resonances in the continuous and discrete systems are revealed.     

Transition factor method for discrete master equations; and application to chemical reactions

We introduce transition factors and derive equations for them which are equivalent to the originalN-dimensional discrete master equation. After transition to continuous variables we obtain nonlocal partial differential equations for these transition factors which are slowly varying variables. Finally we consider a chemical reaction system. Using this method the corresponding master equation is exactly solvable in a very simple manner.     

Two-dimensional spherical oscillator in a constant magnetic field

We study the equations of motion of a spherical oscillator model suggested by Bellucci and Nersessian, in the presence of a constant magnetic field. This model is shown to be exactly solvable classically in contrast to the Higgs oscillator which is not exactly solvable in magnetic fields.     

Knots,links, braids and exactly solvable models in statistical mechanics

We present a general method to construct the sequence of new link polynomials and its two variable extension from exactly solvable models in statistical mechanics. First, we find representations of the braid group from the Boltzmann weights of the exactly solvable models. Second, we give the Markov traces associated with new braid group representations and using them construct new link polynomials. Third, we extend the theory into a two-variable version of the new link polynomials. Throughout the paper, we emphasize the essential roles played by the exactly solvable models and the underlying Yang-Baxter relation.     

Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions

We construct a class of exactly solvable generalized Kitaev spin-1/2 models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-1/2 model can be mapped to a gas of free Majorana fermions coupled to static Z2 gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional(2D) tetragon-octagon model and a three dimensional(3D) xy bond model are studied.