二维薛定谔对称性和三维呼吸子与Kelvin波纹复合体作为准大质量Nambu-Goldstone模
Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
摘要：
被限制在二维简谐势阱中的玻色-爱因斯坦凝聚体（BEC）具有隐藏的二维薛定谔对称性，即被囚禁势修正的薛定谔对称性。这种对称性的自发破缺引起BEC的呼吸运动，其振荡频率由谐波陷阱的强度鲁棒地确定。在本文中，我们证明了2D薛定谔对称性的概念可以应用于预测的性质的三维（3D）集体模式传播沿凝聚限制在一个细长的陷阱。我们发现了三种集体模，它们的存在是由薛定谔对称性鲁棒地保证的，它们在物理上被解释为一个呼吸模和两个开尔文波纹复模，即，涡核和凝结水表面相互作用振荡的复合模式。利用Bogoliubov理论[D. A. Takahashi和M. Nitta，Ann.Phys.354，101（2015）]。此外，我们指出这些模可以解释为“准大质量Nambu-Goldstone（NG）模”，即它们同时具有准NG模和大质量NG模的性质：准NG模出现在拉格朗日量的一部分对称性自发破缺时，而大质量NG模出现在修正对称性自发破缺时.
英文摘要：
Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonic trap are known to possess a hidden 2D Schrödinger symmetry, that is, the Schrödinger symmetry modified by a trapping potential. Spontaneous breaking of this symmetry gives rise to a breathing motion of the BEC, whose oscillation frequency is robustly determined by the strength of the harmonic trap. In this paper, we demonstrate that the concept of the 2D Schrödinger symmetry can be applied to predict the nature of three dimensional (3D) collective modes propagating along a condensate confined in an elongated trap. We find three kinds of collective modes whose existence is robustly ensured by the Schrödinger symmetry, which are physically interpreted as one breather mode and two Kelvin-ripple complex modes, i.e., composite modes in which the vortex core and the condensate surface oscillate interactively. We provide analytical expressions for the dispersion relations (energy-momentum relation) of these modes using the Bogoliubov theory [D. A. Takahashi and M. Nitta, Ann. Phys. 354, 101 (2015)]. Furthermore, we point out that these modes can be interpreted as "quasi-massive-Nambu-Goldstone (NG) modes", that is, they have the properties of both quasi-NG and massive NG modes: quasi-NG modes appear when a symmetry of a part of a Lagrangian, which is not a symmetry of full a Lagrangian, is spontaneously broken, while massive NG modes appear when a modified symmetry is spontaneously broken.
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