The relation between one-to-one correspondent orthonormal eigenstates of H0 and H(λ) ＝ H0 + λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local ...The relation between one-to-one correspondent orthonormal eigenstates of H0 and H(λ) ＝ H0 + λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local destruction due to nonlinear resonance. Numerical results are given to show such possibility with a special Jacobi diagonalization method. The conclusions show that for the system H(λ) belonging to the same class as H0, the relation between one-to-one correspondent orthonormal eigenstates |φi(λ)> and|φ0m(i)>can be expressed as an analytical unitary matrix which can be identified to the relevant quantum canonical transformation. But for the system H(λ) violated dynamical symmetry, the relation between one-to-one correspondent orthonormal eigenstates cannot be expressed as an analytical unitary matrix. Such a kind of unitary matrix cannot be taken as a quantum canonical transformation to define quantum mechanical quantities. This is a key point for studying the quantum chaos with the help of dynamical symmetry theory.展开更多
Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),sel...Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),self-steepening(SS),and stimulated Raman scattering are considered only perturbatively,In this paper,we study the existence of the TOD-and SS-induced soliton solutions.The existence conditions of the TOD-and SS-induced bright and dark solitons are quite different from those of the GVD-and SPM-induced solitons.展开更多
文摘The relation between one-to-one correspondent orthonormal eigenstates of H0 and H(λ) ＝ H0 + λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local destruction due to nonlinear resonance. Numerical results are given to show such possibility with a special Jacobi diagonalization method. The conclusions show that for the system H(λ) belonging to the same class as H0, the relation between one-to-one correspondent orthonormal eigenstates |φi(λ)> and|φ0m(i)>can be expressed as an analytical unitary matrix which can be identified to the relevant quantum canonical transformation. But for the system H(λ) violated dynamical symmetry, the relation between one-to-one correspondent orthonormal eigenstates cannot be expressed as an analytical unitary matrix. Such a kind of unitary matrix cannot be taken as a quantum canonical transformation to define quantum mechanical quantities. This is a key point for studying the quantum chaos with the help of dynamical symmetry theory.
文摘Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),self-steepening(SS),and stimulated Raman scattering are considered only perturbatively,In this paper,we study the existence of the TOD-and SS-induced soliton solutions.The existence conditions of the TOD-and SS-induced bright and dark solitons are quite different from those of the GVD-and SPM-induced solitons.
