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 Book 1946)

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.

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.

Cover 1 Lecture Notes in Mathematics 1946 2 Quantum Transport 4 ISBN: 978-3-540-79573-5 5 Preface 7 Contents 11 Periodic Homogenization and Effective Mass Theorems for the Schrödinger Equation 15 Mathematical Properties of Quantum Evolution Equations 59 Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle 124 Multiscale Computations for Flow and Transport in Heterogeneous Media 182 List of Participants 262 LIST OF C.I.M.E. SEMINARS 265 Lecture Notes in Mathematics 269 Front Matter....Pages I-XIV Periodic Homogenization and Effective Mass Theorems for the Schrödinger Equation....Pages 1-44 Mathematical Properties of Quantum Evolution Equations....Pages 45-109 Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle....Pages 111-168 Multiscale Computations for Flow and Transport in Heterogeneous Media....Pages 169-248 Back Matter....Pages 249-251 In this volume, a result of The CIME Summer School held in Cetraro, Italy, in 2006, four leading specialists present different aspects of quantum transport modeling. It provides an excellent basis for researchers in this field.