On a one-dimensional Schrödinger-Poisson scattering model

Naoufel Ben Abdallah; Pierre Degond; Peter A. Markowich

doi:10.1007/pl00001463

On a one-dimensional Schrödinger-Poisson scattering model

Naoufel Ben Abdallah^*, Pierre Degond, Peter A. Markowich

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

79 Scopus citations

Abstract

A Schrödinger - Poisson model describing the stationary behavior of a quantum device away from equilibrium is proposed and analyzed. In this model, current carrying scattering states of the Schrödinger equation are considered. The potential is coupled to the Schrödinger equation through the density matrix defined according to a prescribed statistics. Existence of solutions is proven. The semiclassical limit is performed via a Wigner transform which leads to the standard boundary value problem for the semiclassical Vlasov-Poisson system. Finally, a high injection asymptotics is investigated.

Original language	English (US)
Pages (from-to)	135-155
Number of pages	21
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	48
Issue number	1
DOIs	https://doi.org/10.1007/pl00001463
State	Published - Jan 1997
Externally published	Yes

Keywords

Current carrying state
Inflow boundary condition
Quantum phenomena
Semiclassical unit
Vlasov equation
Wigner transform

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1007/pl00001463

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title = "On a one-dimensional Schr{\"o}dinger-Poisson scattering model",

abstract = "A Schr{\"o}dinger - Poisson model describing the stationary behavior of a quantum device away from equilibrium is proposed and analyzed. In this model, current carrying scattering states of the Schr{\"o}dinger equation are considered. The potential is coupled to the Schr{\"o}dinger equation through the density matrix defined according to a prescribed statistics. Existence of solutions is proven. The semiclassical limit is performed via a Wigner transform which leads to the standard boundary value problem for the semiclassical Vlasov-Poisson system. Finally, a high injection asymptotics is investigated.",

keywords = "Current carrying state, Inflow boundary condition, Quantum phenomena, Semiclassical unit, Vlasov equation, Wigner transform",

author = "Abdallah, {Naoufel Ben} and Pierre Degond and Markowich, {Peter A.}",

year = "1997",

month = jan,

doi = "10.1007/pl00001463",

language = "English (US)",

volume = "48",

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T1 - On a one-dimensional Schrödinger-Poisson scattering model

AU - Abdallah, Naoufel Ben

AU - Degond, Pierre

AU - Markowich, Peter A.

PY - 1997/1

Y1 - 1997/1

N2 - A Schrödinger - Poisson model describing the stationary behavior of a quantum device away from equilibrium is proposed and analyzed. In this model, current carrying scattering states of the Schrödinger equation are considered. The potential is coupled to the Schrödinger equation through the density matrix defined according to a prescribed statistics. Existence of solutions is proven. The semiclassical limit is performed via a Wigner transform which leads to the standard boundary value problem for the semiclassical Vlasov-Poisson system. Finally, a high injection asymptotics is investigated.

AB - A Schrödinger - Poisson model describing the stationary behavior of a quantum device away from equilibrium is proposed and analyzed. In this model, current carrying scattering states of the Schrödinger equation are considered. The potential is coupled to the Schrödinger equation through the density matrix defined according to a prescribed statistics. Existence of solutions is proven. The semiclassical limit is performed via a Wigner transform which leads to the standard boundary value problem for the semiclassical Vlasov-Poisson system. Finally, a high injection asymptotics is investigated.

KW - Current carrying state

KW - Inflow boundary condition

KW - Quantum phenomena

KW - Semiclassical unit

KW - Vlasov equation

KW - Wigner transform

UR - http://www.scopus.com/inward/record.url?scp=0031538201&partnerID=8YFLogxK

U2 - 10.1007/pl00001463

DO - 10.1007/pl00001463

M3 - Article

AN - SCOPUS:0031538201

SN - 0044-2275

VL - 48

SP - 135

EP - 155

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 1

ER -

On a one-dimensional Schrödinger-Poisson scattering model

Abstract

Keywords

ASJC Scopus subject areas

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