For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （...For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.展开更多
We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of co...We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.展开更多
Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75...Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.展开更多
By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can b...By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.展开更多
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mo...Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.展开更多
A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation metho...A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method. The results obtained are extensions of Chicone’s for the three dimensional non-Hamiltonian systems.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070358009)
文摘For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.
基金supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No.10475657
文摘We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.
基金supported by the National Natural Science Foundation of China (Grant No. 10574060)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.
基金National Natural Science Foundation of China under grant No.10775097the President Foundation of the Chinese Academy of Sciences
文摘By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.
基金the President Foundation of the Chinese Academy of Sciencesthe Specialized Research Fund for the Doctoral Program of Higher Education
文摘Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.
文摘A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method. The results obtained are extensions of Chicone’s for the three dimensional non-Hamiltonian systems.
