We examine the time development of a wavepacket in a Non-Hermitian PT symmetric tight-bindingchain based on the Bethe ansatz solutions.The complete orthogonal sets in both unbroken and broken PT symmetryregions are es...We examine the time development of a wavepacket in a Non-Hermitian PT symmetric tight-bindingchain based on the Bethe ansatz solutions.The complete orthogonal sets in both unbroken and broken PT symmetryregions are established with respect to an inner product in terms of CPT conjugation.The dynamical development ofa stationary wavepacket is exhibited,showing the impacts from additional imaginary potentials within unbroken andbroken symmetric regimes.Our result indicates that there are distinct dynamic characteristics for both two regions.Theunbroken symmetric imaginary end potentials can be regarded as a special kind of boundary condition in the sense ofHermitian quantum mechanics.展开更多
In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invarianc...In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
The definition and the criterion for a unified symmetry of nonholonomic mechanical systems of non- Chetaev＇s type with unilateral constraints are presented based on the total time derivative along the trajectory of t...The definition and the criterion for a unified symmetry of nonholonomic mechanical systems of non- Chetaev＇s type with unilateral constraints are presented based on the total time derivative along the trajectory of the system. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced froth the unified symmetry, is obtained. An example is given to illustrate the application of the results.展开更多
We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non...We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non singular symmetric matrix for given target eigenvalues using a singular symmetric matrix as the initial matrix for the iteration. Explicit computations are performed for 2 x 2 non singular symmetric matrix to illustrate the result.展开更多
基金Support by the CNSF Grants Nos.10874091 and 2006CB921205
文摘We examine the time development of a wavepacket in a Non-Hermitian PT symmetric tight-bindingchain based on the Bethe ansatz solutions.The complete orthogonal sets in both unbroken and broken PT symmetryregions are established with respect to an inner product in terms of CPT conjugation.The dynamical development ofa stationary wavepacket is exhibited,showing the impacts from additional imaginary potentials within unbroken andbroken symmetric regimes.Our result indicates that there are distinct dynamic characteristics for both two regions.Theunbroken symmetric imaginary end potentials can be regarded as a special kind of boundary condition in the sense ofHermitian quantum mechanics.
文摘In this paper, the Lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the Lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.
文摘The definition and the criterion for a unified symmetry of nonholonomic mechanical systems of non- Chetaev＇s type with unilateral constraints are presented based on the total time derivative along the trajectory of the system. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced froth the unified symmetry, is obtained. An example is given to illustrate the application of the results.
文摘We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non singular symmetric matrix for given target eigenvalues using a singular symmetric matrix as the initial matrix for the iteration. Explicit computations are performed for 2 x 2 non singular symmetric matrix to illustrate the result.
