AN ASYMPTOTIC MODEL FOR THE TRANSPORT OF AN ELECTRON GAS IN A SLAB

被引：1

作者：

Delebecque, Fanny ^{[1
]}

机构：

[1] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse 9, France

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2011年 / 21卷 / 07期

关键词：

Schrodinger-Poisson system; asymptotic analysis; singular perturbation; time averaging; quantum transport; slab; nanoelectronics; SCHRODINGER-POISSON SYSTEM; QUANTUM-MECHANICS; RATE-EQUATIONS; BLOCH MODEL; DYNAMICS; FORCE;

D O I：

10.1142/S0218202511005453

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1443 / 1478

页数：36

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