Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sen...Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.展开更多
A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schr?dinger equation is presented,which describes different kinds of vortex structures.The dynamics of d...A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schr?dinger equation is presented,which describes different kinds of vortex structures.The dynamics of different vortex clusters,such as the single vortex,vortex pair,vortex dipole and vortex trimer in a two-dimensional quantum fluid are analytically studied based on these exact solutions.The time evolutions of the wave of such vortices are demonstrated,and the orbits of motion of singular points in the vortices are also explored.The interactions of vortices in many-vortex clusters are discussed.A repulsive interaction between vortices with the same topological charge,and inter-annihilation and inter-creation of vortices with opposite topological charge,are shown.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10275023）, and by the Science Foundation of the Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China （Grant No T152504）.
文摘Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.
基金the National Natural Science Foundation of China under Grant Nos 10904035 and 11175064the Foundation from the Ministry of Education of China under Grant No 757204003the Foundation of Central High University.
文摘A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schr?dinger equation is presented,which describes different kinds of vortex structures.The dynamics of different vortex clusters,such as the single vortex,vortex pair,vortex dipole and vortex trimer in a two-dimensional quantum fluid are analytically studied based on these exact solutions.The time evolutions of the wave of such vortices are demonstrated,and the orbits of motion of singular points in the vortices are also explored.The interactions of vortices in many-vortex clusters are discussed.A repulsive interaction between vortices with the same topological charge,and inter-annihilation and inter-creation of vortices with opposite topological charge,are shown.
