Exact Methods in Low-dimensional Statistical Physics and Quantum Computing: Lecture Notes of the Les Houches Summer School: Volume 89, July 2008 [Kõva köide]

In the 21 chapters here, Jacobsen (theoretical physics, U. Paris Sud, France) et al. bring together physicists, mathematicians, and other scientists from North America and Europe who gave lectures on exact solutions in low-dimensional theoretical physics at the 89th session of Les Houches Summer School in Grenoble, France, held June through August 2008. The lecture notes address such concepts as the interplay between conformal field theory and stochastic Loewner evolution, Coulomb gas techniques, tiling models, dimers, the definition of models of random curves on a background of random triangulations, boundary conditions, quantum inverse scattering, spin chains, the interplay between integrable models and combinatorics, mass transport models of condensation in real space, quantum impurity problems, the physics of spin liquids, the quantum Hall effect, models of rotating Bose-Einstein condensates, and models of topological order with applications to quantum computing. There is no index. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics.