Quantum hydrodynamics for semiconductors in the high-field case

P. Markowich; C. Ringhofer

doi:10.1016/0893-9659(94)90069-8

Quantum hydrodynamics for semiconductors in the high-field case

P. Markowich^*, C. Ringhofer

^*Corresponding author for this work

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

6 Scopus citations

Abstract

We derive a quantum hydrodynamic model from a relaxation time approximation of the quantum Boltzmann equation by mean-free path asymptotics. The (formal) asymptotics are carried out in the case of a large electric field. They give a linear model for the position, current and energy densities of the electron gas.

Original language	English (US)
Pages (from-to)	37-41
Number of pages	5
Journal	Applied Mathematics Letters
Volume	7
Issue number	5
DOIs	https://doi.org/10.1016/0893-9659(94)90069-8
State	Published - Sep 1994
Externally published	Yes

Keywords

Moment hierarchy
Quantum Boltzmann equation
Small mean free path asymptotics

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/0893-9659(94)90069-8

Cite this

@article{9f9ef4de89f84a13b8d7e6dcb8ce5309,

title = "Quantum hydrodynamics for semiconductors in the high-field case",

abstract = "We derive a quantum hydrodynamic model from a relaxation time approximation of the quantum Boltzmann equation by mean-free path asymptotics. The (formal) asymptotics are carried out in the case of a large electric field. They give a linear model for the position, current and energy densities of the electron gas.",

keywords = "Moment hierarchy, Quantum Boltzmann equation, Small mean free path asymptotics",

author = "P. Markowich and C. Ringhofer",

note = "Funding Information: The first author acknowledges support from the EC-Network #ERBCHRXCT 930413 and from the project entitled {\textquoteleft}Mathematische Analysis und Numerik von Quantenhydrodynamischen Modellen der Halbleiderphysik{\textquoteright} funded by the Deutsche Forschungsgemeinschaft.",

year = "1994",

month = sep,

doi = "10.1016/0893-9659(94)90069-8",

language = "English (US)",

volume = "7",

pages = "37--41",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Limited",

number = "5",

}

TY - JOUR

T1 - Quantum hydrodynamics for semiconductors in the high-field case

AU - Markowich, P.

AU - Ringhofer, C.

N1 - Funding Information: The first author acknowledges support from the EC-Network #ERBCHRXCT 930413 and from the project entitled ‘Mathematische Analysis und Numerik von Quantenhydrodynamischen Modellen der Halbleiderphysik’ funded by the Deutsche Forschungsgemeinschaft.

PY - 1994/9

Y1 - 1994/9

N2 - We derive a quantum hydrodynamic model from a relaxation time approximation of the quantum Boltzmann equation by mean-free path asymptotics. The (formal) asymptotics are carried out in the case of a large electric field. They give a linear model for the position, current and energy densities of the electron gas.

AB - We derive a quantum hydrodynamic model from a relaxation time approximation of the quantum Boltzmann equation by mean-free path asymptotics. The (formal) asymptotics are carried out in the case of a large electric field. They give a linear model for the position, current and energy densities of the electron gas.

KW - Moment hierarchy

KW - Quantum Boltzmann equation

KW - Small mean free path asymptotics

UR - http://www.scopus.com/inward/record.url?scp=0039969047&partnerID=8YFLogxK

U2 - 10.1016/0893-9659(94)90069-8

DO - 10.1016/0893-9659(94)90069-8

M3 - Article

AN - SCOPUS:0039969047

SN - 0893-9659

VL - 7

SP - 37

EP - 41

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 5

ER -

Quantum hydrodynamics for semiconductors in the high-field case

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this