High density limit of the stationary one dimensional Schrödinger-Poisson system

Details High density limit of the stationary one dimensional Schrödinger-Poisson system High density limit of the stationary one dimensional Schrödinger-Poisson system

2010-05-17

arxiv.org/abs/1005.2889v1

SIAM Journal on Multiscale Modeling and Simulation 7, 1 (2008) 124-146

Mathematics

Analysis of PDEs

Scientific paper

The stationary one dimensional Schr\"odinger-Poisson system on a bounded interval is considered in the limit of a small Debye length (or small temperature). Electrons are supposed to be in a mixed state with the Boltzmann statistics. Using various reformulations of the system as convex minimization problems, we show that only the first energy level is asymptotically occupied. The electrostatic potential is shown to converge towards a boundary layer potential with a profile computed by means of a half space Schr\"odinger-Poisson system.

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