Quantum Transport

Modelling, Analysis and Asymptotics — Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 11–16, 2006

  • Grégoire Allaire
  • Anton Arnold
  • Pierre Degond
  • Thomas Yizhao Hou
  • Naoufel Ben Abdallah
  • Giovanni Frosali

Part of the Lecture Notes in Mathematics book series (LNM, volume 1946)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pierre Degond, Samy Gallego, Florian Méhats, Christian Ringhofer
    Pages 111-168
  3. Yalchin Efendiev, Thomas Yizhao Hou
    Pages 169-248
  4. Back Matter
    Pages 249-251

About this book


The CIME Summer School held in Cetraro, Italy, in 2006 addressed researchers interested in the mathematical study of quantum transport models.

In this volume, a result of the above mentioned Summer School, four leading specialists present different aspects of quantum transport modelling. Allaire introduces the periodic homogenization theory, with a particular emphasis on applications to the Schrödinger equation. Arnold focuses on several quantum evolution equations that are used for quantum semiconductor device simulations. Degond presents quantum hydrodynamic and diffusion models starting from the entropy minimization principle. Hou provides the state-of-the-art survey of the multiscale analysis, modelling and simulation of transport phenomena.

The volume contains accurate expositions of the main aspects of quantum transport modelling and provides an excellent basis for researchers in this field.


Excel Homogenization theory Mathematica Multiple scale problems Open quantum systems Quantum evolution equations. Schrödinger equation Volume computation entropy evolution homogenization modelling open quantum system theorem

Authors and affiliations

  • Grégoire Allaire
    • 1
  • Anton Arnold
    • 2
  • Pierre Degond
    • 3
  • Thomas Yizhao Hou
    • 4
  1. 1.Centre de Mathématiques AppliquéesEcole PolytechniquePalaiseau CedexFrance
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria
  3. 3.Institut de MathématiquesUniversité de ToulouseToulouse Cedex 9France
  4. 4.Applied and Computational Math. 217-50California Institute of TechnologyPasadenaUSA

Editors and affiliations

  • Naoufel Ben Abdallah
    • 1
  • Giovanni Frosali
    • 2
  1. 1.Institut de MathématiquesUniversité de ToulouseToulouse Cedex 9France
  2. 2.Dipartimento di Matematica ApplicataUniversità di FirenzeFirenzeItaly

Bibliographic information

  • DOI
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-79573-5
  • Online ISBN 978-3-540-79574-2
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site
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