With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

Quantum Theory: Density, Condensation, and Bonding presents in a unitary manner the main actual theories of matter, mainly the density function theory (DFT) for fermions, the Bose-Einstein condensation (BEC) for bosons, and chemical bonding as a special realization of the first two so-called mixed fermionic-bosonic states. The book covers the modern and ultimately developed quantum theories involving the key concepts of density, condensation, and bonding. The book compiles, for the first time, the density functional theory with Bose-Einstein condensation and chemical bonding theories in a fresh and novel perspective. The book introduces modern theories of matter structure and explains the nature of chemical bonds under the consecrated and ultimate quantum paradigms of molecular structure. The book is divided into three parts, one for each level of studies: Part I: Primer Density Functional Theory is suitable for undergraduate introductory courses in physics, chemistry, and the natural sciences. Part II: Primer Density Functional Bose-Einstein Condensation Theory would be suitable for graduate- or master-level courses in physics or natural sciences. Part III: Modern Quantum Theories of Chemical Bonding is written for the post-graduate, master or doctorate courses on quantum structure of molecules in chemistry or natural sciences. Thus, this book is organized as a succession of three linked courses, from undergraduate, to graduate, to postgraduate levels in modern quantum theories of many-body systems. It covers three main concepts: density, condensation, and bonding and contains the most celebrated and challenging theories of matter. The book provides a fresh perspective on the quantum theory of structure of physico-chemical systems and will show students at all levels and researchers the way for future elaboration and discoveries toward the unification of the physical and chemical concepts of matter.

The correlations between physical systems provide significant information about their collective behaviour – information that is used as a resource in many applications, e.g. communication protocols. However, when it comes to the exploitation of such correlations in the quantum world, identification of the associated ‘resource’ is extremely challenging and a matter of debate in the quantum community. This dissertation describes three key results on the identification, detection, and quantification of quantum correlations. It starts with an extensive and accessible introduction to the mathematical and physical grounds for the various definitions of quantum correlations. It subsequently focusses on introducing a novel unified picture of quantum correlations by taking a modern resource-theoretic position. The results show that this novel concept plays a crucial role in the performance of collaborative quantum computations that is not captured by the standard textbook approaches. Further, this new perspective provides a deeper understanding of the quantum-classical boundary and paves the way towards establishing a resource theory of quantum computations.

Jesse Joe Jacks was born sometime during the snow blizzard of 1923. The Lower Elk County game warden died from a lightning strike on July 23, 1959. Olan Chapman came to life in August of 1974 and found a computer career with a center city, electronics firm. Jacks loved nature and lived to protect wild life. Jesse Joe was also a crack shot with a firearm - any firearm. Olan Chapman attended the theater, played piano and once led a march against the National Rifle Association Jacks fought in the Korean War and never drank anything stronger than beer. Chapman battled a war from within, and never sipped anything lighter than rum and coke. Both men had the same fingerprints, much to the chagrin of Lt General Alexis Grumman, federal director for para normal activities. QUANTUM ROOTS is based on the belief that people form from recycled energy.

The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.

This book constitutes the refereed proceedings of the Third International Workshop on Post-Quantum Cryptography, PQCrypto 2010, held in Darmstadt, Germany, in May 2010. The 16 revised full papers presented were carefully reviewed and selected from 32 submissions. The papers are organized in topical sections on cryptanalysis of multivariate systems, cryptanalysis of code-based systems, design of encryption schemes, and design of signature schemes.

Recently, analogies between laboratory physics (e.g. quantum optics and condensed matter) and gravitational/cosmological phenomena such as black holes have attracted an increasing interest. This book contains a series of selected lectures devoted to this new and rapidly developing field. Various analogies connecting (apparently) different areas in physics are presented in order to bridge the gap between them and to provide an alternative point of view.