The self-consistent Bloch-equation in one dimension

Norbert Mauser; Anton Arnold; Peter A. Markowich

doi:10.1016/0898-1221(91)90099-P

The self-consistent Bloch-equation in one dimension

Norbert Mauser^*, Anton Arnold, Peter A. Markowich

^*Corresponding author for this work

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

1 Scopus citations

Abstract

We give a mathematical analysis of a simplified model to calculate an equilibrium density matrix of electrons. Under the assumption of Boltzmann statistics, the Bloch equation is coupled to the Poisson equation. Existence and uniqueness of a solution of the resulting non-linear parabolic equation is proven.

Original language	English (US)
Pages (from-to)	197-202
Number of pages	6
Journal	Computers and Mathematics with Applications
Volume	21
Issue number	2-3
DOIs	https://doi.org/10.1016/0898-1221(91)90099-P
State	Published - 1991
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Modeling and Simulation

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10.1016/0898-1221(91)90099-P

Cite this

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title = "The self-consistent Bloch-equation in one dimension",

abstract = "We give a mathematical analysis of a simplified model to calculate an equilibrium density matrix of electrons. Under the assumption of Boltzmann statistics, the Bloch equation is coupled to the Poisson equation. Existence and uniqueness of a solution of the resulting non-linear parabolic equation is proven.",

author = "Norbert Mauser and Anton Arnold and Markowich, {Peter A.}",

year = "1991",

doi = "10.1016/0898-1221(91)90099-P",

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volume = "21",

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T1 - The self-consistent Bloch-equation in one dimension

AU - Mauser, Norbert

AU - Arnold, Anton

AU - Markowich, Peter A.

PY - 1991

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N2 - We give a mathematical analysis of a simplified model to calculate an equilibrium density matrix of electrons. Under the assumption of Boltzmann statistics, the Bloch equation is coupled to the Poisson equation. Existence and uniqueness of a solution of the resulting non-linear parabolic equation is proven.

AB - We give a mathematical analysis of a simplified model to calculate an equilibrium density matrix of electrons. Under the assumption of Boltzmann statistics, the Bloch equation is coupled to the Poisson equation. Existence and uniqueness of a solution of the resulting non-linear parabolic equation is proven.

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U2 - 10.1016/0898-1221(91)90099-P

DO - 10.1016/0898-1221(91)90099-P

M3 - Article

AN - SCOPUS:44949281474

SN - 0898-1221

VL - 21

SP - 197

EP - 202

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2-3

ER -

The self-consistent Bloch-equation in one dimension

Abstract

ASJC Scopus subject areas

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