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 gen...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 generalboundary 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.展开更多
The coherent states of parabose oscillator of order p based on the well-known Green's ansatz have been constructed. Furthermore, it is shown that the completeness relation for these coherent states may be expresse...The coherent states of parabose oscillator of order p based on the well-known Green's ansatz have been constructed. Furthermore, it is shown that the completeness relation for these coherent states may be expressed in the form of 2×2 matrix.展开更多
Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theres...Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.展开更多
We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obt...We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.展开更多
The Ott-Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscil- lators. However, previous works using the ansatz only focused on the evolution of the order parameter and th...The Ott-Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscil- lators. However, previous works using the ansatz only focused on the evolution of the order parameter and the information on desynchronized oscillators is less discussed. In this work, we show that the Ott-Antonsen ansatz can also be applied to investigate the desynchronous dynamics in coupled phase oscillators. Studying the original Kuramoto model and two of its variants, we find that the dynamics of α（ω）, the coefficient in the Fourier series of the probability density, can give most of the information on the synchronization, for example, the threshold of natural frequency delimiting the oscillators synchronized and desychronized by the mean field, the formulation of the effective frequency ωe （ω） of desynchronous oscillators, and the structure of the graph ωe （ω）.展开更多
In the framework of graded quantum inverse scattering method, we obtain the eigenvalues and the eigenvectors of the Osp(l|2) model with reflecting boundary conditions in FBF background. The corresponding Bathe ansatz ...In the framework of graded quantum inverse scattering method, we obtain the eigenvalues and the eigenvectors of the Osp(l|2) model with reflecting boundary conditions in FBF background. The corresponding Bathe ansatz equations are obtained.展开更多
We present three diagonal reflecting matrices for the CN vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue an...We present three diagonal reflecting matrices for the CN vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.展开更多
In this article, the solitary wave and shock wave solitons for nonlinear Ostrovsky equation and Potential Kadomstev-Petviashvili equations have been obtained. The solitary wave ansatz is used to carry out the solutions.
The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
We construct an integrable 1D extended Hubbard model within the framework of the quantum inverse scattering method.With the help of the nested algebraic Bethe ansatz method,the eigenvalue Hamiltonian problem is solved...We construct an integrable 1D extended Hubbard model within the framework of the quantum inverse scattering method.With the help of the nested algebraic Bethe ansatz method,the eigenvalue Hamiltonian problem is solved by a set of Bethe ansatz equations,whose solutions are supposed to give the correct energy spectrum.展开更多
Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exac...Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.展开更多
(接53卷第5期)5.2第二篇。图4是矩阵力学三部曲第二篇的截图。这篇长31页的论文分为五个部分:导言;第一章,矩阵计算;第二章,动力学;第三章,检验非简谐振子;第四章,电动力学评论。文章的作者为玻恩和约当。此文目的是把海森堡上一篇论文...(接53卷第5期)5.2第二篇。图4是矩阵力学三部曲第二篇的截图。这篇长31页的论文分为五个部分:导言;第一章,矩阵计算;第二章,动力学;第三章,检验非简谐振子;第四章,电动力学评论。文章的作者为玻恩和约当。此文目的是把海森堡上一篇论文中的Ansatze发展成量子力学的系统理论(zu einer systematischen Theorie der Quantenmechanik)。展开更多
文摘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 generalboundary 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.
文摘The coherent states of parabose oscillator of order p based on the well-known Green's ansatz have been constructed. Furthermore, it is shown that the completeness relation for these coherent states may be expressed in the form of 2×2 matrix.
文摘Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.
文摘We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.
基金Supported by the National Natural Science Foundation of China under Grant Nos 71301012 and A050105
文摘The Ott-Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscil- lators. However, previous works using the ansatz only focused on the evolution of the order parameter and the information on desynchronized oscillators is less discussed. In this work, we show that the Ott-Antonsen ansatz can also be applied to investigate the desynchronous dynamics in coupled phase oscillators. Studying the original Kuramoto model and two of its variants, we find that the dynamics of α（ω）, the coefficient in the Fourier series of the probability density, can give most of the information on the synchronization, for example, the threshold of natural frequency delimiting the oscillators synchronized and desychronized by the mean field, the formulation of the effective frequency ωe （ω） of desynchronous oscillators, and the structure of the graph ωe （ω）.
基金supported by the Mathematics and Physics Foundation of Beijing Polytechnic University and the National Natural Science Foundation of China (Grant No 40536029)
文摘Explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.
文摘In the framework of graded quantum inverse scattering method, we obtain the eigenvalues and the eigenvectors of the Osp(l|2) model with reflecting boundary conditions in FBF background. The corresponding Bathe ansatz equations are obtained.
文摘We present three diagonal reflecting matrices for the CN vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.
文摘In this article, the solitary wave and shock wave solitons for nonlinear Ostrovsky equation and Potential Kadomstev-Petviashvili equations have been obtained. The solitary wave ansatz is used to carry out the solutions.
文摘The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
基金Financial support from the National Natural Science Foundation of China(Grant Nos.12105221,12175180,12074410,12047502,11934015,11975183,11947301,11775177,11775178 and 11774397)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB33000000)+4 种基金the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSZ005)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant Nos.2021JCW-19,2017KCT-12 and 2017ZDJC-32)the Scientific Research Program Funded by the Shaanxi Provincial Education Department(Grant No.21JK0946)the Beijing National Laboratory for Condensed Matter Physics(Grant No.202162100001)the Double First-Class University Construction Project of Northwest University is gratefully acknowledged.
文摘We construct an integrable 1D extended Hubbard model within the framework of the quantum inverse scattering method.With the help of the nested algebraic Bethe ansatz method,the eigenvalue Hamiltonian problem is solved by a set of Bethe ansatz equations,whose solutions are supposed to give the correct energy spectrum.
文摘Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.
文摘(接53卷第5期)5.2第二篇。图4是矩阵力学三部曲第二篇的截图。这篇长31页的论文分为五个部分:导言;第一章,矩阵计算;第二章,动力学;第三章,检验非简谐振子;第四章,电动力学评论。文章的作者为玻恩和约当。此文目的是把海森堡上一篇论文中的Ansatze发展成量子力学的系统理论(zu einer systematischen Theorie der Quantenmechanik)。
