Description
Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled ?The logic of quantum mechanics? quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results. Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.
Audience
Libraries, scholars from various fields as logic, philosophy of science, mathematics, physics, computer science, artificial intelligence
Contents
Foreword (A. Dvurecenskij) Editorial Preface (K. Engesser, D. Gabbay and D. Lehmann) New Quantum Structures (A. Dvurecenskij) Quantum Structures and Fuzzy Set Theory (J. Pykasz) Algebraic and Measure-theoretic Properties of Classes of Subspaces of an Inner Product Space (D. Buhagiar, E. Chetcuti and A. Dvurecenskij) Quantum Probability (S. Gudder) Orthomodular Lattices and Orthomodular Posets (P. Ptak and S. Pulmannova) Quantum Logic and Partially Ordered Abelian Groups (D.J. Foulis and R.J. Greechie) Operator Algebras (J. Hamhalter) Constructions of Quantum Structures (M. Navara) D-Posets (F. Chovanec and F. Kopka) Wigner's Theorem and its Generalisations (G. Chevalier) Hilbert Lattices (I. Stubbe and B. van Steirteghem) Ortholattice Equations and Hilbert Lattices (R. Mayet) Decomposition in QL (J. Harding) Starting from the Convex Set of States (E. Beltrametti) QL and Automata Theory (M. Ying) QL and Quantum Computation (N.D. Megill and M. Pavicic) Index
Bibliographic & ordering Information
Hardbound, 820 pages, publication date: AUG-2007
ISBN-13: 978-0-444-52870-4
ISBN-10: 0-444-52870-9
Included in series
Les Houches Summer School Proceedings,
Description
There has been recently some interdisciplinary convergence on a number of precise topics which can be considered as prototypes of complex systems. This convergence is best appreciated at the level of the techniques needed to deal with these systems, which include: 1) A domain of research around a multiple point where statistical physics, information theory, algorithmic computer science, and more theoretical (probabilistic) computer science meet: this covers some aspects of error correcting codes, stochastic optimization algorithms, typical case complexity and phase transitions, constraint satisfaction problems. 2) The study of collective behavior of interacting agents, its impact on understanding some types of economical and financial problems, their link to population and epidemics dynamics, game theory, social, biological and computer networks and evolution. The present book is the written version of the lectures given during the Les Houches summer school session on "Complex Systems", devoted to these emerging interdisciplinary fields. The lectures consist both in a number of long methodological courses (probability theory, statistical physics of disordered systems, information theory, network structure and evolution, agent-based economics and numerical methods) and more specific, 'problem oriented' courses. Lecturers are all leading experts in their field; they have summarized recent results in a clear and authoritative manner. The "Les Houches lecture notes" have a long tradition of excellence and are often found to be useful for a number of years after they were written. The book is of interest to students and researchers with various backgrounds: probability theory, computer science, information theory, physics, finance, biology, etc.
Audience
University libraries, Students, researchers, European networks and research centers on "Complexity"
Contents
Chapter 1 - Monasson: Introduction to phase transitions in random optimization problems Chapter 2 - Montanari-Urbanke: Modern Coding Theory: The Statistical Mechanics and Computer Science Points of View Chapter 3 - Parisi: Mean field theory of Spin Glasses: Statics and Dynamics Chapter 4 - Majumdar: Random Matrices, The Ulam Problem, Directed Polymer and Growth Models, and Sequence Matching Chapter 5 - Kirman: Economies with Interacting Agents Chapter 6 - Sethna: Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the Renormalization Group Chapter 7 - Toninelli: Bootstrap and Jamming Percolation Chapter 8 - Newman: Complex Networks Chapter 9 - Challet: Minority Games Chapter 10 - Giardina: Metastable States in Glassy Systems Chapter 11 - Fisher: Evolutionary Dynamics Chapter 12 - Berg: Statistical modelling and analysis of biological networks Chapter 13 - Berthier: The slow dynamics of glassy materials: Insights from computer simulations Chapter 14 - Franceschelli: Epigenetic landscape and catastrophe theory Chapter 15 - Zdeborova: A Hike in the Phases of the 1-in-3 satisfiability
Bibliographic & ordering Information
Hardbound, 526 pages, publication date: AUG-2007
ISBN-13: 978-0-444-53006-6
ISBN-10: 0-444-53006-1
Series: Progress in Mathematical Physics , Vol. 52
2007, Approx. 145 p., Hardcover
ISBN: 978-3-7643-8523-1
About this book
This book starts with a detailed introduction to general relativity by world expert T. Damour. It includes a review of what may lie beyond by string theorist I. Antoniadis, and collects up-to-date essays on the experimental tests of this theory.
Contrary to some beliefs, general relativity is now a theory extremely well confirmed by detailed experiments, including the precise timing of the double pulsar J0737-3039 explained by M. Kramer, member of the team which discovered it in 2003, and satellite missions such as Gravity Probe B described by leading team member J. Mester. The search for detecting gravitational waves is also very much under way as reviewed by J.-Y. Vinet.
Written for:
Theoretical and mathematical physicists, cosmologists, astrophysicists
Keywords:
general relativity
gravitational wave astronomy
pulsar
Table of contents
Series: Progress in Mathematical Physics , Vol. 53
2007, Approx. 215 p., Hardcover
ISBN: 978-3-7643-8521-7
About this book
This book starts with an introduction by V. Pasquier on the usefulness of non-commutative geometry, especially in the condensed matter context of the Hall effect. This theme is further developped by A. Polychronakos, which together with L. Susskind introduced the concept of non-commutative fluids.
Jean-Michel Maillet compares the experimental results on one dimensional magnetic chains to the theoretical predictions based on the algebraic Bethe Ansatz and related to quantum group symmetries that he actively developped with many collaborators.
On the high energy side of non-commutative geometry the book includes two complementary reviews. A. Connes describes the striking progress recently made in gathering all the interactions and fields of the standard model into a non-commutative geometry on a simple internal space, while V. Rivasseau describes in a large review the very recent technique of renormalization of quantum field theories on non-commutative space-time, which lead to the surprising discovery of their improved short-distance behavior.
Written for:
Theoretical and mathematical physicists, geometers, high energy physicists
Keywords:
noncommutative fluids
noncommutative geometry
quantum Hall effect
quantum space
Table of contents
Preface.- Introduction.- Non-commutative Renormalization.- Non-commutative Fluids.- Quantum Groups for Diffusion Experiments with Neutrons.- Non-commutative Geometry and the Spectral Model of Space-Time.