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 aspes of quantum transport modelling. Allaire introduces the periodic homogenization theory, with a particular emphasis on applications to the Schrodinger equation. Arnold focuses on several quantum evolution equations that are used for quantum semiconductor vice 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 volumcontains accurate expositions of the main aspects of quantum transport modelling and provides an excellent basis for researchers in this field.

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