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

Abstract

The Gross-Pitaevskii (GP) or nonlinear Schrödinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possess 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 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 independently of the details of the system. We further construct an exact effective action for all the NG modes.

7 pages, 3 figures, 2 ancillary files, references added, published version

References in corpus (6)

• Nonrelativistic conformal field theories
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
• Counting rule of Nambu-Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach
• Nambu-Goldstone Modes Propagating along Topological Defects: Kelvin and Ripple Modes from Small to Large Systems
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes

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