双势阱中玻色-爱因斯坦凝聚系统不动点分析

Analysis of the fixed point for two components Bose-Einstein condensates in a double-well potential

在准经典理论下,研究双势阱中的两组分玻色-爱因斯坦凝聚系统的动力学属性。利用平均场近似写出该量子系统的经典哈密顿量,通过数值及线性化分析,找到系统的对称型、反对称型、各向同性型及非对称型共四类不动点。分别讨论两种特殊模式下的不动点数目的变化情况和稳定性,发现两种模式出现不动点数目的上下限,且两种模式下不动点的稳定性与对应系数矩的阵特征值有关。

The dynamic properties of the two components Bose-Einstein condensates system in a double-well potential is studied within classical theory in this paper. The mean-field approxima- tion is used to write the classical Hamiltonian of the quantum system, and then the numerical and linear analysis is used to find four types of the fixed point., symmetrical, antisymmetrical, iso- tropic and asymmetrical. The variety of the fixed point number and their stability of the two spe- cial modes are discussed. The results show that the stability of the fixed point is related to the ei- genvalues of the matrix.