Quantum Transport : Modelling Analysis and Asymptotics — Lectures given at the C.I.M.E. Summer School held in Cetraro Italy September 11–16 2006 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. Periodic Homogenization and Effective Mass Theorems for the Schrödinger 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.