A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM...A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy.展开更多
By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-f...By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-form identity.展开更多
Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplin...Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.展开更多
Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the d...Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.展开更多
The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this pape...The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.展开更多
A type of higher-dimensionaJ loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarch...A type of higher-dimensionaJ loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarchy of equations, is obtained by taking use of the zero curvature equation, whose Hamiltonian structure is worked out by employing the constructed quadratic identity.展开更多
In this paper, the assignment of acomplex 8-spin-half system （7,7-dichloro-6-oxo-2-tio-bicycle [3.2.0] heptane-4-carboxlic acid） using nuclear magnetic resonance （NMR） techniques is presented and the hamiltonian o...In this paper, the assignment of acomplex 8-spin-half system （7,7-dichloro-6-oxo-2-tio-bicycle [3.2.0] heptane-4-carboxlic acid） using nuclear magnetic resonance （NMR） techniques is presented and the hamiltonian obtained, was used to demonstrate universal control. The system has 313C and 51H,in our work, we carried out traditional 1-D and 2-D experiments and also made use of coherent control together with simulation to get the full hamiltonian of this weakly coupled system. Spin-echo J-resolved 2-D experiments were used to obtain the heteronuclear and homonuclear coupling values; COSY45 experiments were used to obtain the signs of homonuclear coupling constants. The signs of heteronuclear coupling constants were obtained using the polarization transfer method. All the data obtained in the experiments were used in the simulation of the 1-D spectra and then optimized using the least square fitting method. After obtaining the full hamiltonian of the 8-spin system, we used it in QIP, prepared pseudopure states and implemented 1-qubit and 2-qubit gates on one of its 6-qubit subsystems.展开更多
Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ（6） is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is de...Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ（6） is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems.展开更多
We study the influence of screening effect on quantum decoherence for charge qubit and the process of quantum information storage. When the flux produced by the circulating current in SQUID loop is considered, screeni...We study the influence of screening effect on quantum decoherence for charge qubit and the process of quantum information storage. When the flux produced by the circulating current in SQUID loop is considered, screening effect is formally characterized by a LC resonator. Using large-detuning condition and Fr6hlich transformation in the qubit-cavity-resonator system, we calculate the decoherenee factor for charge qubit and the effective qubit-cavity Hamiltonian. The decoherence factor owns a factorized structure, it shows that screening effect is a resource of decoherence for charge qubit. The effective Hamiltonian shows that the screening effect results in a frequency shift for charge qubit and a modified qubit-cavity coupling constant induced by a LC resonator.展开更多
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational iden...A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.展开更多
A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding bro...A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.展开更多
We study the dynamics of the multipartite systems nonresonantly interacting with electromagnetic fields, focusing on the large detuning limit for the effective Hamiltonian. Due to the many-particle interference effect...We study the dynamics of the multipartite systems nonresonantly interacting with electromagnetic fields, focusing on the large detuning limit for the effective Hamiltonian. Due to the many-particle interference effects, the more rigorous large detuning condition for neglecting the rapidly oscillating terms for the effective Plamiltonian should be △ 〉〉 N^1/2 g, instead of △ 〉〉 g usually used in the literature even in the case of multipartite systems, with N the number of microparticles involved, g the coupling strength, A the detuning. This result is significant since merely the satisfaction of the original condition will result in the invalidity of the effective Hamiltonian and the errors of the parameters associated with the detuning in the multipartite case.展开更多
文摘A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101Key Disciplines of Shanghai Municipality (S30104)
文摘By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-form identity.
文摘Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.
基金Supported by the National Science Foundation of China under Grant No.10971031the Natural Science Foundation of Shandong Province under Grant No.ZR2009AL021
文摘Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.
文摘The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.
基金Supported by the Scientific Research Ability Foundation for Young Teacher of Northwest Normal University under Grant No.NWNULKQN -10-25
文摘A type of higher-dimensionaJ loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarchy of equations, is obtained by taking use of the zero curvature equation, whose Hamiltonian structure is worked out by employing the constructed quadratic identity.
文摘In this paper, the assignment of acomplex 8-spin-half system （7,7-dichloro-6-oxo-2-tio-bicycle [3.2.0] heptane-4-carboxlic acid） using nuclear magnetic resonance （NMR） techniques is presented and the hamiltonian obtained, was used to demonstrate universal control. The system has 313C and 51H,in our work, we carried out traditional 1-D and 2-D experiments and also made use of coherent control together with simulation to get the full hamiltonian of this weakly coupled system. Spin-echo J-resolved 2-D experiments were used to obtain the heteronuclear and homonuclear coupling values; COSY45 experiments were used to obtain the signs of homonuclear coupling constants. The signs of heteronuclear coupling constants were obtained using the polarization transfer method. All the data obtained in the experiments were used in the simulation of the 1-D spectra and then optimized using the least square fitting method. After obtaining the full hamiltonian of the 8-spin system, we used it in QIP, prepared pseudopure states and implemented 1-qubit and 2-qubit gates on one of its 6-qubit subsystems.
基金Supported by the Nature Science Foundation of Shandong Province of China under Grant No.ZR.2009GM005the Science and Technology Plan Project of the Educational Department of Shandong Province of China under Grant No.J09LA54the research project of "SUST Spring Bud" of Shandong University of Science and Technology of China under Grant No.2009AZZ071
文摘Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ（6） is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems.
基金Supported by National Natural Science Foundation of China under Grant Nos. 0547101 and 10604002
文摘We study the influence of screening effect on quantum decoherence for charge qubit and the process of quantum information storage. When the flux produced by the circulating current in SQUID loop is considered, screening effect is formally characterized by a LC resonator. Using large-detuning condition and Fr6hlich transformation in the qubit-cavity-resonator system, we calculate the decoherenee factor for charge qubit and the effective qubit-cavity Hamiltonian. The decoherence factor owns a factorized structure, it shows that screening effect is a resource of decoherence for charge qubit. The effective Hamiltonian shows that the screening effect results in a frequency shift for charge qubit and a modified qubit-cavity coupling constant induced by a LC resonator.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159)+3 种基金the Chunhui Plan of the Ministry of Education of Chinathe Innovation Project of Zhejiang Province (No.T200905)the Natural Science Foundation of Shanghai (No.09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)
文摘A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.
基金supported by the National Natural Science Foundation of China(Grant No.11125420)the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.
基金Supported by National Natural Science Foundation of China under Grant No.10774192
文摘We study the dynamics of the multipartite systems nonresonantly interacting with electromagnetic fields, focusing on the large detuning limit for the effective Hamiltonian. Due to the many-particle interference effects, the more rigorous large detuning condition for neglecting the rapidly oscillating terms for the effective Plamiltonian should be △ 〉〉 N^1/2 g, instead of △ 〉〉 g usually used in the literature even in the case of multipartite systems, with N the number of microparticles involved, g the coupling strength, A the detuning. This result is significant since merely the satisfaction of the original condition will result in the invalidity of the effective Hamiltonian and the errors of the parameters associated with the detuning in the multipartite case.
