Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes

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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.

元の言語English
記事番号051601
ジャーナルPhysical Review A
96
発行部数5
DOI
出版物ステータスPublished - 2017 11 7

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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