We investigate the stability and excitations of two-dimensional circular-symmetry exciton-polariton condensates. The system is described by the circular-symmetry dissipative Gross-Pitaevskii (GP) equation based on the meanfield theory. The excitation properties around the steady-state is analytically calculated by means of the standard Bogoliubov-de Gennes (BdG) approach. We discuss the stability and modulational instability conditions which are determined by the parameters of the system and the parameters that characterize the Gaussian steady-state. We find that, the square of a parameter ¯ι plays a crucial role in characterizing the stability criterion and the excitaion spectrum.
The motion of soliton centroid in two-dimensional (2D) Bose-Einstein condensate (BEC) is investigated by using the time-dependent variational method in this paper. Similar to the classical 2D harmonic oscillator’s motion equation, the Gaussian trial function with wavepacket centroid coordinates is chosen to get the motion equation of centroid. The Lissajous figures of trajectory are discovered for the first time by solving the motion equations of different initial conditions. This not only proves that the matter wave soliton possesses the motion characteristics of classical particles and shows macroscopic quantum properties, but also provides a new tool for the study of BEC.
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