Conformal symmetry and the nonlinear Schrodinger equation

Details Conformal symmetry and the nonlinear Schrodinger equation Conformal symmetry and the nonlinear Schrodinger equation

2001-02-27

arxiv.org/abs/cond-mat/0102488v3

Phys.Rev. A65 (2002) 012103

Physics

Condensed Matter

RevTeX, 5 pages (v1); Added a footnote and an example (v2); Updated references, to appear in Physical Review A (v3)

Scientific paper

10.1103/PhysRevA.65.012103

We show that the width of the wave-packet of a class of generalized nonlinear Schrodinger equations (NLSE) trapped in an arbitrary time-dependent harmonic well in any dimensions is universally determined by the same Hill's equation. This class of generalized NLSE is characterized by a dynamical O(2,1) symmetry in absence of the trap. As an application, we study the dynamical instabilities of the rotating as well as non-rotating Bose-Einstein condensates in one and two dimensions. We also show exact extended parametric resonance in a non-relativistic Chern-Simons theory producing a gauged NLSE.

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