Abstract
We consider the 2d and 3d many body Schrödinger equations in the presence of anisotropic switchable quadratic traps. We extend and improve the collapsing estimates in Klainerman-Machedon [24] and Kirkpatrick-Schlein-Staffilani [23]. Together with an anisotropic version of the generalized lens transform in Carles [3], we derive rigorously the cubic NLS with anisotropic switchable quadratic traps in 2d through a modified Elgart-Erdös-Schlein-Yau procedure. For the 3d case, we establish the uniqueness of the corresponding Gross-Pitaevskii hierarchy without the assumption of factorized initial data.
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