Quantum Transport. Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11-16, 2006 12+

📖 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 Hydro...