Semiclassical wave-packets for weakly nonlinear Schrödinger equations with rotation

Abstract

We consider semiclassically scaled, weakly nonlinear Schrödinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating quantum gases. We construct asymptotic solutions in the form of semiclassical wave-packets, which are concentrated in both space and in frequency around an classical Hamiltonian phase-space flow. The rotation term is thereby seen to alter this flow, but not the corresponding classical action.

13 pages; some typos corrected; new remark 2.6 added; new reference included regarding remark 2.6