2017/05/31 by Keisuke Ohashi, Toshiaki Fujimori, Muneto Nitta · 22 citations
Physics and Astronomy · #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Equations of motion #Harmonic oscillator #Mathematical physics #Noether's theorem #Oscillation (cell signaling) #Physics #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #Symmetry (geometry) #Symmetry breaking #cond-mat.quant-gas #hep-th
paper · pdf · doi:10.1103/physreva.96.051601
published in Physical Review A 96(5) (American Physical Society) · 7 pages, 3 figures, 2 ancillary files, references added, published version
openalex publication_date 2017/11/07 · arxiv created 2017/11/10 · arxiv updated 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Gross-Pitaevskii or nonlinear Schr"odinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possesses a modified Schr"odinger 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 Schr"odinger symmetry. We show that the Noether theorem for the modified Schr"odinger 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.