Breathing modes and hidden symmetry of trapped atoms in two dimensions

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Abstract
Atoms confined in a harmonic potential show universal oscillations in two dimensions (2D). We point out the connection of these ``breathing'' modes to the presence of a hidden symmetry. The underlying symmetry SO(2,1), i.e., the two-dimensional Lorentz group, allows pulsating solutions to be constructed for the interacting quantum system and for the corresponding nonlinear Gross-Pitaevskii equation. We point out how this symmetry can be used as a probe for recently proposed experiments of trapped atoms in 2D.

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