Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
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俘获玻色-爱因斯坦凝聚体和大质量南部-戈德斯通模式的共形对称性
DOI：
10.1103/physreva.96.051601
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Muneto Nitta
中科院分区：
文献类型：
--
作者：
Keisuke Ohashi;Toshiaki Fujimori;Muneto Nitta
与超冷原子气态玻色-爱因斯坦凝聚相关的Gross-Pitaevskii或非线性薛定谔方程在二维空间中具有修正的薛定谔对称性，存在谐波捕获势，（人工）恒定磁场（或旋转）和平方静电势的（人工）电场。我们发现，一个方差和一个中心的被困气体有或没有涡可以被视为大规模的南武-戈德斯通（NG）模式与自发破缺的修改薛定谔对称性。我们表明，修改后的薛定谔对称性的Noether定理给出了通用的运动方程，它描述了准确的时间演化的被困气体，如谐波振荡，回旋运动，和呼吸振荡的频率由对称性独立的系统的细节。我们进一步构造了所有NG模式的精确有效作用量。
The Gross-Pitaevskii or nonlinear Schrödinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possesses a modified Schrödinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation), and an (artificial) electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu-Goldstone (NG) modes associated with spontaneous breaking of the modified Schrödinger symmetry. We show that the Noether theorem for the modified Schrödinger symmetry gives universal equations of motion which describe exact time evolutions of the trapped gases such as a harmonic oscillation, a cyclotron motion, and a breathing oscillation with frequencies determined by the symmetry independent of the details of the system. We further construct an exact effective action for all the NG modes.