Operator Algebras And Quantum Statistical Mechanics Ii

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Operator Algebras And Quantum Statistical Mechanics 1

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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-05-27

Operator Algebras And Quantum Statistical Mechanics 1 written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-27 with Mathematics categories.

This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.

Operator Algebras And Quantum Statistical Mechanics Ii

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Author : Ola Bratteli
language : en
Publisher:
Release Date : 2014-01-15

Operator Algebras And Quantum Statistical Mechanics Ii written by Ola Bratteli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Operator Algebras And Quantum Statistical Mechanics Ii

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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Operator Algebras And Quantum Statistical Mechanics Ii written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.

In this chapter, and the following one, we examine various applications of C*-algebras and their states to statistical mechanics. Principally we analyze the structural properties of the equilibrium states of quantum systems con sisting of a large number of particles. In Chapter 1 we argued that this leads to the study of states of infinite-particle systems as an initial approximation. There are two approaches to this study which are to a large extent comple mentary. The first approach begins with the specific description of finite systems and their equilibrium states provided by quantum statistical mechanics. One then rephrases this description in an algebraic language which identifies the equilibrium states as states over a quasi-local C*-algebra generated by sub algebras corresponding to the observables of spatial subsystems. Finally, one attempts to calculate an approximation of these states by taking their limit as the volume of the system tends to infinity, the so-called thermodynamic limit. The infinite-volume equilibrium states obtained in this manner provide the data for the calculation of bulk properties of the matter under considera tion as functions of the thermodynamic variables. By this we mean properties such as the particle density, or specific heat, as functions of the temperature and chemical potential, etc. In fact, the infinite-volume data provides a much more detailed, even microscopic, description of the equilibrium phenomena although one is only generally interested in the bulk properties and their fluctuations.

Operator Algebras And Quantum Statistical Mechanics Ii

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Author : Ola Bratteli
language : en
Publisher:
Release Date : 1981

Operator Algebras And Quantum Statistical Mechanics Ii written by Ola Bratteli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.

Operator Algebras And Quantum Statistical Mechanics

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Author : Ola Bratteli
language : en
Publisher:
Release Date : 1981

Operator Algebras And Quantum Statistical Mechanics written by Ola Bratteli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Operator algebras categories.

Operator Algebras And Quantum Statistical Mechanics

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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Operator Algebras And Quantum Statistical Mechanics written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.

For almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMS-condition and stability, quantum spin systems and continuous systems. Major changes in the new edition relate to Bose--Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Notes and remarks have been considerably augmented.

C Algebras And W Algebras

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Author : Shoichiro Sakai
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

C Algebras And W Algebras written by Shoichiro Sakai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." (Math. Reviews) "In theory, this book can be read by a well-trained third-year graduate student - but the reader had better have a great deal of mathematical sophistication. The specialist in this and allied areas will find the wealth of recent results and new approaches throughout the text especially rewarding." (American Scientist) "The title of this book at once suggests comparison with the two volumes of Dixmier and the fact that one can seriously make this comparison indicates that it is a far more substantial work that others on this subject which have recently appeared"(BLMSoc)

Tomita Takesaki Theory In Algebras Of Unbounded Operators

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Author : Atsushi Inoue
language : en
Publisher: Springer
Release Date : 2006-11-14

Tomita Takesaki Theory In Algebras Of Unbounded Operators written by Atsushi Inoue and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.

Open Quantum Systems I

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Author : Stéphane Attal
language : en
Publisher: Springer
Release Date : 2006-08-18

Open Quantum Systems I written by Stéphane Attal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Mathematics categories.

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.