Bøger i Theoretical and Mathematical Physics serien

This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts:Part One: Classical Dynamical SystemsAddresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity.Includes a survey of the theory of simple perceptrons and their storage capacity.Part Two: Quantum Dynamical SystemsFocuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems.Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom.Introduces a model ofquantum perceptron whose storage capacity is computed and compared with the classical one.Part Three: Quantum Dynamical Entropies and ComplexitiesDevoted to quantum dynamical entropies and algorithmic complexities.This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.

The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

This popular, often cited text returns in a softcover edition to provide a thorough introduction to statistical physics and thermodynamics, and to exhibit the universality of the chain of ideas leading from the laws of microphysics to the macroscopic behaviour of matter.

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics.

Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Since the appearance of these standard texts many books (both physical and mathematical) on the non relativistic Schrodinger equation have been published, but only very few on the Dirac equation.

Study Edition

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of variousmodels with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories.

From the reviews:"...useful for experts in mathematical physics...this is a very interesting book, which deserves to be found in any physical library." (OPTICS & PHOTONICS NEWS, July/August 2005).

This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required.

This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached.

Clearly structured in an intuitive way, this volume provides and overview of relativistic quantum mechanics. A thorough discussion of the one particle concept within relativistic quantum mechanics, including its limitations, is provided.

Providing an introduction to mathematical aspects of quantum information and open systems, this volume provides a unique combination of applications to bio- and nano-systems. Readers will find a new paradigm for quantum computation, as well as introductory treatment of functional analysis.

The most important extensions are due to my practical experience as a risk manager in the German Savings Banks' As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added.

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds.

The Institute for Theoretical Physics at Utrecht University quickly responded to this new challenge and created an international master's programme in Theoret ical Physics which started running in the summer of 2000.

This is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom.

Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles.

"Many-Body Problems and Quantum Field Theory".

This monograph on fluid mechanics is not only a superb and unique textbook but also an impressive piece of research. It is the only textbook that fully covers turbulence, all the way from the works of Kolmogorov to modern dynamics.

This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.

In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. This second edition of the successful textbook adds various new sections on relativistic quantum chemistry and on the relativistic treatment of the proton in hydrogen.

Relativity plays an important role in atomic nuclei, and, since the early 1970s, there has been increasing interest in, and literature on, the nucleus as a relativistic system. Directed to advanced students and researchers, it explains both the underlying relativistic theory and compares predictions with actual experiments.

Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.

Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry, as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods.

Intended as a compendium for physicists and mathematicians on coherent states and their applications, this volume moves from the basic mathematical structures of generalized coherent states to specific examples of coherent states such as the hydrogen atom.

In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.

This thorough volume is the perfect foundation for intermediate-level research in string theory. Its pedagogic and self-contained structure raises is a step up from results compendia and features more advanced topics including conformal field theory.

Are you looking for a concise summary of the theory of Schroedinger operators? Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don't just cover general properties, but also detail multiparticle quantum mechanics - including bound states of Coulomb systems and scattering theory.

In retrospect, the first edition of this book now seems like a mere sketch for a book. Among the more obvious changes, this edition contains a new section on Kruskal space, another on the plane gravitational wave, and a third on linearized general relativity;