This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.

This multi-authored textbook addresses graduate students with a background in physics, mathematics or computer science. No research experience is necessary. Consequently, rather than comprehensively reviewing the vast body of knowledge and literature gathered in the past twenty years, this book concentrates on a number of carefully selected aspects of quantum information theory and technology. Given the highly interdisciplinary nature of the subject, the multi-authored approach brings together different points of view from various renowned experts, providing a coherent picture of the subject matter. The book consists of ten chapters and includes examples, problems, and exercises. The first five present the mathematical tools required for a full comprehension of various aspects of quantum mechanics, classical information, and coding theory. Chapter 6 deals with the manipulation and transmission of information in the quantum realm. Chapters 7 and 8 discuss experimental implementations of quantum information ideas using photons and atoms. Finally, chapters 9 and 10 address ground-breaking applications in cryptography and computation.

Quantum Kinetic Equations; H. Spohn. Microscopic Derivation of Hydrodynamics with Phase Transition in a Plasma Model; G.L. Sewell. Ferromagnetism in Itinerant Electron Systems; H. Tasaki. Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimabll Model; T. Kennedy. Diffusive Limit of the Asymmetric Simple Exclusion; R. Esposito, et al. Weak Coupling Limit; L.J. Landau. Limit Laws for Recurrence Times in Expanding Maps of an Interval; P. Collet. Stochastic Geometric Aspects of Some Quantum Spin Chains; B. Nachtergaele. The Species Totally Asymmetric Simple Exclusion Process; E.R. Speer. How to Reconstruct a Heat Bath; B. Kummerer. Interacting Particle Systems on Non-Commutative Spaces; T. Matsui. Non-Self-Averaging Effects in Sums of Random Variables, Spin Glasses, Random Maps, and Random Walks; B. Derrida. Quantum Adiabatic Evolution; A. Joye, C.E. Pfister. 48 additional articles. Index.

A unique and accessible book providing a unified framework for studying quantum and classical dynamical systems, both finite and infinite, conservative and dissipative. Many examples and references are included throughout, making it an ideal text for graduate students in physics and mathematics.