Collapsing Estimates and the Rigorous Derivation of the 2d Cubic Nonlinear Schrödinger Equation with Anisotropic Switchable Quadratic Traps

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.

v6, 32 pages. Added an algebraic explanation of the generalized lens transform using the metaplectic representation. Accepted to appear in Journal de Mathématiques Pures et Appliquées. Comments are welcomed

References in corpus (3)

• Rigorous Derivation of the Gross-Pitaevskii Equation
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Second order corrections to mean field evolution for weakly interacting Bosons in the case of 3-body interactions

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