Mean-field dynamics of rotating bosons in strongly anisotropic traps

The effective equations describing the mean-field dynamics of bosons in a rotating anisotropic trap are derived rigorously. It is shown that in the mean-field/strong anisotropy limit, the dynamics of an initial state that is close to a ground state of the dominant one dimensional harmonic potential is effectively decoupled, such that in the orthogonal complement of the direction of the dominant potential, it is described by a two dimensional magnetic nonlinear Schrodinger equation. Depending on the scaling of the two-body interaction, the nonlinear dynamics is given by a Hartree or the Gross-Pitaevskii equation in a rotating reference frame. For the sake of clarity of presentation, the Hartree case is discussed first before extending the analysis to the Gross-Pitaevskii one. The rigorous analysis yields explicit error bounds and new precise estimates of finite size effects.