Quantum transport : modelling, analysis and asymptotics : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11-16, 2006
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書誌事項
Quantum transport : modelling, analysis and asymptotics : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11-16, 2006
（Lecture notes in mathematics, 1946）
Springer, c2008
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注記
"Frondazione C.I.M.E."
Includes bibliographical references
内容説明・目次
内容説明
Downscaling of semiconductor devices, which is now reaching the nanometer scale, makes it mandatory for us to understand the quantum phenomena - volvedinchargetransport.Indeed,fornanoscaledevices,thequantumnature of electrons cannot be neglected. In fact, it underlies the operation of an increasing number of devices. Unlike classical transport, the intuition of the physicistandtheengineerisbecominginsu?cientforpredictingthenatureof device operation in the quantum context-the need for su?ciently accurate and numerically tractable models represents an outstanding challenge in which applied mathematics can play an important role. TheCIMESession"QuantumTransport:Modelling,AnalysisandAsy- totics", which took place in Cetraro (Cosenza), Italy, from September 11 to September 16, 2006, was intended both to present an overview of up-to-date mathematical problems in this ?eld and to provide the audience with te- niques borrowed from other ?elds of application. It was attended by about 50 scientists and researchers, coming from d- ferent countries. The list of participants is included at the end of this book.
The school was structured into four courses: ' * Gr' egoire Allaire (Ecole Polytechnique, Palaiseau, France) Periodic - mogeneization and E?ective MassTheorems for theSchr. odinger Equation. * AntonArnold(TechnischeUniversit. at,Vienna)MathematicalProperties of Quantum Evolution Equations. * Pierre Degond (Universit' e Paul Sabatier and CNRS, Toulouse, France) Quantum Hydrodynamic and Di?usion Models Derived from the Entropy Principle. * Thomas Yizhao Hou (Caltech, Los Angeles, USA) Multiscale Com- tations for Flow and Transport in Heterogeneous Media. This book contains the texts of the four series of lectures presented at the Summer School. Here follows a brief description of the subjects of these courses.
目次
Periodic Homogenization and Effective Mass Theorems for the Schroedinger Equation.- Mathematical Properties of Quantum Evolution Equations.- Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle.- Multiscale Computations for Flow and Transport in Heterogeneous Media.
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