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

Bibliographical note

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.

Keywords

Moment hierarchy
Quantum Boltzmann equation
Small mean free path asymptotics

ASJC Scopus subject areas

Applied Mathematics

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10.1016/0893-9659(94)90069-8

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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",

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

language = "English (US)",

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pages = "37--41",

journal = "Applied Mathematics Letters",

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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

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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

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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