The rigorous derivation of the ${\mathbb{T}}^2$ focusing cubic NLS from 3D

Abstract

We derive rigorously the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics describing a dilute Bose gas with periodic boundary condition in the $x$-direction and a well of infinite-depth in the $z$-direction. Physical experiments for these systems are scarce. We find that, to fulfill the empirical requirement for observing NLS dynamics in experiments, namely, the kinetic energy dominates the potential energy, it is necessary to impose an extra restriction on the system parameters. This restriction gives rises to an unusual coupling constant.

arXiv commentv2, improved result

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• Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space
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• On the nonlinear Schrödinger equation with a toroidal trap in the strong confinement regime
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate