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Quantum Transport

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

  • Book
  • © 2008

Overview

Authors:
  1. Grégoire Allaire

    1. Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau Cedex, France

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  2. Anton Arnold

    1. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien, Austria

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  3. Pierre Degond

    1. Institut de Mathématiques, Université de Toulouse, Toulouse Cedex 9, France

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  4. Thomas Yizhao Hou

    1. Applied and Computational Math. 217-50, California Institute of Technology, Pasadena, USA

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Editors:
  1. Naoufel Ben Abdallah

    1. Institut de Mathématiques, Université de Toulouse, Toulouse Cedex 9, France

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  2. Giovanni Frosali

    1. Dipartimento di Matematica Applicata, Università di Firenze, Firenze, Italy

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

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Periodic Homogenization and Effective Mass Theorems for the Schrödinger Equation

    • Grégoire Allaire
    Pages 1-44

  3. Mathematical Properties of Quantum Evolution Equations

    • Anton Arnold
    Pages 45-109

  4. Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle

    • Pierre Degond, Samy Gallego, Florian Méhats, Christian Ringhofer
    Pages 111-168

  5. Multiscale Computations for Flow and Transport in Heterogeneous Media

    • Yalchin Efendiev, Thomas Yizhao Hou
    Pages 169-248

  6. Back Matter

    Pages 249-251
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Keywords

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.

Authors, Editors and Affiliations

  • Institut de Mathématiques, Université de Toulouse, Toulouse Cedex 9, France

    Naoufel Ben Abdallah, Pierre Degond

  • Dipartimento di Matematica Applicata, Università di Firenze, Firenze, Italy

    Giovanni Frosali

  • Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau Cedex, France

    Grégoire Allaire

  • Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien, Austria

    Anton Arnold

  • Applied and Computational Math. 217-50, California Institute of Technology, Pasadena, USA

    Thomas Yizhao Hou

Bibliographic Information

  • Book Title: Quantum Transport

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

  • Authors: Grégoire Allaire, Anton Arnold, Pierre Degond, Thomas Yizhao Hou

  • Editors: Naoufel Ben Abdallah, Giovanni Frosali

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-79574-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2008

  • Softcover ISBN: 978-3-540-79573-5Published: 13 August 2008

  • eBook ISBN: 978-3-540-79574-2Published: 03 July 2008

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 260

  • Number of Illustrations: 57 b/w illustrations

  • Topics: Partial Differential Equations, Quantum Physics, Classical Mechanics, Fluid- and Aerodynamics

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