High density limit of the stationary one dimensional Schr\"odinger-Poisson system
Analysis of PDEs
2010-05-31 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1005.2889,
title = {High density limit of the stationary one dimensional Schr\"odinger-Poisson system},
author = {Raymond El Hajj and Naoufel Ben Abdallah},
journal= {arXiv preprint arXiv:1005.2889},
year = {2010}
}