二维玻色-爱因斯坦凝聚磁激子的真、准和不稳定Nambu Goldstone模
True, quasi and unstable Nambu Goldstone modes of the twodimensional Bose Einstein condensed magnetoexcitons
摘要：
在Bogoliubov准平均理论的框架下，研究了波矢为零的玻色-爱因斯坦凝聚体中二维磁激子的集体元激发。位于最低朗道能级的电子和空穴的哈密顿量包含由于粒子到激发朗道能级和返回的虚量子跃迁而产生的补充相互作用。结果，磁激子零波数之间的相互作用并不消失，它们的BEC变得稳定。能谱只包含一个无间隙的，真正的第二类南布戈德斯通模式，在小的波数值描述的光学等离子体激元型振荡的波数平方成正比。有两个激子类型的分支对应于正常和异常的格林函数。这两种模式的间隙与roton型段在中间值的波矢量，可以命名为准NG模式。第四个分支是声学等离子体激元型模式，在波矢的小值和中间值的区域中具有绝对不稳定性。所有分支在波矢量的大值处具有饱和型依赖性。真NG模的数目和种类与对称性破缺算符的数目一致。
英文摘要：
The collective elementary excitations of two dimensional magnetoexcitons in a Bose Einstein condensate with zero wavevector are investigated in the framework of the Bogoliubov theory of quasi averages. The Hamiltonian of the electrons and holes lying in the lowest Landau levels contains supplementary interactions due to virtual quantum transitions of the particles to the excited Landau levels and back. As a result, the interaction between the magnetoexcitons zero wavenumbers does not vanish and their BEC becomes stable. The energy spectrum contains only one gapless,true Nambu Goldstone mode of the second kind, proportional to the square of wavenumber at small values of wavenumber describing the optical plasmon type oscillations. There are two exciton type branches corresponding to normal and abnormal Green functions. Both modes are gapped with roton type segments at intermediary values of the wavevectors and can be named quasi NG modes. The fourth branch is the acoustical plasmon type mode with absolute instability in the region of small and intermediary values of the wavevectors. All branches have a saturation type dependencies at great values of the wave vectors. The number and the kind of the true NG modes are in accordance with the number of the broken symmetry operators.
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