The rigorous derivation of the T2 focusing cubic NLS from 3D |
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Authors: | Shunlin Shen |
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Affiliation: | 1. School of Mathematical Sciences, Peking University, Beijing, 100871, China;2. Department of Mathematics, University of Rochester, Rochester, NY 14627, USA |
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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, that the kinetic energy dominates the potential energy, it is necessary to impose an extra restriction on the system parameters. This restriction gives rise to an unusual coupling constant. |
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Keywords: | 3D focusing many-body Schrödinger equation 2D focusing nonlinear Schrödinger equation BBGKY hierarchy Focusing Gross-Pitaevskii hierarchy |
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