Asymptotic Bethe ansatz for the Sutherland–Römer model with open boundary conditions

By constructing the reflection spin-Dunkl operators, the integrable Sutherland–Römer model (SRM) with open boundary condition is established, which describes a one-dimensional, two-component, quantum many-particle system in which like particles interact with a pair potential g(g+1)/sinh²(r), while unlike particles interact with a pair potential −g(g+1)/cosh²(r). By solving the Schrödinger equation and using the properties of the hypergeometric functions and gamma functions, the two-particle scattering matrix and the reflection matrix are obtained in the framework of the asymptotic Bethe ansatz method. The Bethe ansatz equations of the system are obtained. The Hamiltonians of SRM with some other open boundary conditions are expressed explicitly. Our method can be generalized, as a example, to the boundary Calogero–Sutherland model which is also constructed by the reflection spin-Dunkl operators.     

Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K^± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.     

On the Graded Quantum Yang-Baxter and Reflection Equations

We clarify the extra signs appearing in the graded quantum Yang-Baxter reflection equations, when they are written in a matrix form. We find the boundary K-matrix for the Perk-Schultz six-vertex model, thus give a general solution to the graded reflection equation associated with it.     

用平面映射边界条件的伽辽金法分析耦合脊形光波导

用平面射映边界条件的伽辽金法分析耦合脊形光波导的结果表明，耦合脊形光波导的耦合能力随脊高增加而减小，随波导间距增加呈指数衰减。给出了耦合脊形光波导所承载的偶、奇模电场分布，其结果与采用其它方法得出的结果吻合得较好，可以优化波导光电子器件的结构参数。另外，平面映射边界条件避免了非物理反射，待求矩阵小，计算效率高。     

N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N=2 supersymmetry. A new boundary reflection matrix is obtained for this model and N=2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N=2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee–Yang model, a massive deformation of the anisotropic Kondo model at the filling values g=2/(2n+3) and the boundary Ashkin–Teller model.     

Quantum Affine Reflection Algebras of Type $$d_n^{\left( 1 \right)}$$ and Reflection Matrices

Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang–Baxter equation). In this paper we use the quantum affine reflection algebras of type to determine new n-parameter families of nondiagonal reflection matrices. These matrices describe the reflection of vector solitons off the boundary in affine Toda field theory. They can also be used to construct new integrable vertex models and quantum spin chains with open boundary conditions.     

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.     

Lax pair formulation for the open boundary Osp(1∣2) spin chain

Based on the Lax pair formulation, we study the integrable conditions of the Osp(1∣2) spin chain with open boundaries. We consider both the non-graded and graded versions of the Osp(1∣2) chain. The Lax pair operators M_± for the boundaries can be induced by the Lax operator M_j for the bulk of the system. They correspond to the reflection equations (RE) and the Yang–Baxter equation, respectively. We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries. The double row monodromy matrix and transfer matrix of the spin chain have also been constructed. The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE. This construction is another way to prove the quantum integrability of the Osp(1∣2) chain. We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.     

Diffraction mechanism of specular reflection of light from photonic crystals

The spectra of specular reflection and diffraction of light for a resonant two-dimensional photonic crystal consisting of semiconductor cylinders embedded in a dielectric matrix, as well as the exciton-polariton band structure of this crystal, are studied theoretically. It is shown that specular reflection of light from a photonic crystal can be considerably enhanced by diffraction in the photonic crystal and reflection from its inner boundary with vacuum.     

The algebraic Bethe ansatz for the Osp(2|2) model with open boundary conditions

We obtain four different diagonal reflecting matrices by solving the reflection equation of the Osp(2|2) model. At the same time, we solve the model with open boundary condition by using the algebraic Bethe ansatz. The procedure of constructing the multi-particle state and achieving the eigenvalue of the transfer matrix and corresponding Bethe equations is presented in detail.     

非镜面膜的椭偏研究

本文提出了SnO_2:F绒面膜的三层膜模型;从表示平面波传播性质的界面矩阵和膜层矩阵出发,导出了三层膜系统的散射矩阵和总反射系数,建立了反射式椭偏术的基本公式;利用反射式椭偏光谱法,测得SnO_2:F绒面膜的厚度和色散关系.     

振荡介质中平面波的反射

在复金慈堡-朗道方程描述的振荡介质中研究了平面波的反射.从理论上给出了产生反射的条件,导出了反射波和入射波这两个区域的分界线与两种介质分界线的夹角.发现两类反射,一类为回折射产生的反射,对于这类反射,理论上给出了反射角;另一类为纯反射,它与折射无关.理论分析与数值模拟结果均表明：只有当入射角大于临界入射角才会发生反射,而且反射角等于临界入射角;对于纯反射,反射角随波频率增大而增大. 关键词： 复金慈堡-朗道方程 平面波 反射     

Notes on integrable boundary interactions of open SU(4) alternating spin chains

Ref. [J. High Energy Phys. 1708, 001(2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena(ABJM)theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001(2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.     

Reflection K-matrices of the 19-vertex model and XXZ spin-1 chain with general boundary terms

We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with . An integrable XXZ spin-1 chain Hamiltonian with general boundary interactions is also obtained.     

固-固无限周期声子晶体中SH波全反射隧穿的谐振理论

利用边界条件推导出SH波在一维固-固声子晶体中的转移矩阵, 得出一维固-固无限周期声子晶体中SH波的色散关系. 通过建立一维固-固无限周期声子晶体的谐振腔模型并利 用共振条件得出SH波的全反射隧穿的波长公式. 利用波长公式研究了SH波全反射隧穿的波长变化规律, 其结果与色散法一致. 解释了一维固-固无限周期声子晶体中SH波的全反射隧穿效应产生的原因. 关键词： 声子晶体 SH波 全反射隧穿 谐振理论     

On the spurious eigenvalues for a concentric sphere in BIEM

In this paper, the null-field integral equation method is employed to study the occurring mechanism of spurious eigenvalues for a concentric sphere. By expanding the fundamental solution into degenerate kernels and expressing the boundary density in terms of spherical harmonics, all boundary integrals can be analytically determined. It is noted that our null-field integral formulation can locate the collocation point on the real boundary thanks to the degenerate kernel. In addition, the spurious eigenvalues are parasitized in the formulations while true eigensolutions are dependent on the boundary condition such as the Dirichlet or Neumann problem. By using the updating term and updating document of singular value decomposition (SVD) technique, true and spurious eigenvalues can be extracted out, respectively. Besides, true and spurious boundary eigenvectors are obtained in the right and left unitary vectors in the SVD structure of the influence matrices. This finding agrees with that of 2D cases.     

一种基于BLT方程的孔缝箱体屏蔽效能计算方法

本文基于等效电路法, 提出一种通过BLT方程计算带孔缝箱体屏蔽效能的方法, 可以快速准确计算任意入射、极化平面波照射箱体以及任意位置开孔和双面开孔箱体的屏蔽效能. 根据等效电路法求解出孔缝散射矩阵, 依据信号流图建立传播关系和散射关系方程, 并推导出包含孔缝耦合效应的广义BLT方程. 将BLT方程计算结果与等效电路法计算结果以及CST仿真做对比, 验证了方法的正确性. 与等效电路法相比, 在同一孔阻抗下, 孔缝散射矩阵包含箱体内外能量之间的相互耦合作用, 本方法计算结果精度更高, 能预测更多箱体谐振模式; 与CST仿真相比, 本方法占用时间和资源少, 可以对箱体参数进行规律性研究.     

幂函数形式连续变截面梁振动的弯曲固有频率分析*

本文使用微分方程解析法求解变截面梁固有频率。首先,建立变截面梁模型,其中截面面积和惯性矩均按幂次函数变化。得到变截面梁自由振动时挠度的解析表达式,并获得不同边界条件下梁弯曲振动的固有频率方程。其中惯性矩所对应幂指数与截面面积的幂指数的差值为4时,可得自振频率方程的精确形式;而幂指数差值不等于4时,给出近似解法。其次,对4种具体的变截面梁求解不同边界下的自振频率,并与瑞利-里兹法所得的自振频率解比较。验证精确解法结果的正确性,并发现近似解法结果的相对偏差在5%以内。该解析方法较瑞利-里兹法具有能快速求解的特点,且易于分析截面参数对梁固有频率的影响。由算例可得,边界和其他参数不变时,梁的同阶次无量纲自振频率随着幂次指数的增加而增加。几何参数中仅截面形状参数改变时,随着形状参数的增加,梁的同阶次无量纲自振频率随之减小,但固定-自由梁的第一阶自振频率除外。     

On diffuse reflection at the boundary for the Boltzmann equation and related equations

The paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities. The solutions obtained are proved to conserve mass at the boundary. After a preliminary study of the collisionless case, the main results obtained are existence for the Boltzmann equation in a DiPerna-Lions framework with the above boundary conditions in a bounded measure sense, and existence together with uniqueness for the BGK equation with Maxwellian diffusion on the boundary in anL framework.Deceased.