科研之友
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摘要
We study the limiting behavior of a Schrodinger-Poisson system describing a three-dimensional quantum gas that is confined along the vertical z-direction in a fine slab. The starting point is the three-dimensional Schrodinger-Poisson system with Dirichlet conditions on two horizontal planes z = 0 and z = epsilon , where the small parameter epsilon is the scale width of the slab. The limit epsilon -> 0 appears to be an infinite system of two-dimensional nonlinear Schrodinger equations. Our strategy combines a refined analysis of the Poisson kernel acting on strongly confined densities and a time-averaging process that allows us to deal with the fast time oscillations.
- 出版日期2011-7
