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Operator Algebras and Quantum Statistical Mechanics 2:

Equilibrium States. Models in Quantum Statistical Mechanics, Volume 2
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Springer, 1997 - Science - 517 pages
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.
  

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Selected pages

Contents

51 Ιntroduction
3
52 Continous Quantum System I
6
522 The CAR and CCR Algebras
15
523 States and Representatives
23
524 The Ideal Fermi Gas
45
525 Τhe Ideal Bose Gas
57
53 KMSStates
76
532 The Set of KMS States
112
623 The Maximum Entropy Principle
266
624 Translationally Invariant States
286
625 Uniqueness of KMS States
306
626 Nonuniqueness of KMS States
317
627 Ground States
338
63 Continuous Quantum Systems II
353
631 Τhe Local Hamiltonians
355
632 Τhe Wiener Intergral
366

533 The Set of Ground States
131
54 Stability and Equilibrium
144
542 Stability and the KMS Condtion
176
543 Gauge Groups and the Chemical Potential
197
544 Passive Systems
211
Note and Remarks
217
Models of Quantum Statistical Mechanics
235
61 Introduction
237
62 Quantum Spin System
239
622 The Gibbs Condition for Equilibrium
261
633 Τhe Thermodynamic Limit I the Reduced Density Matrices
381
634 The Thermodynamic Limit II States and Greens Functions
395
64 Conclusion
422
Notes and Remarks
424
References
463
Book and Monographs
465
Articles
468
List of Symbols
487
Subject Index
499
Copyright

Other editions - View all

Operator Algebras and Quantum Statistical Mechanics 1: C*- and W*-Algebras ...
Operator Algebras and Quantum Statistical Mechanics 1: C*- and W*-Algebras ...
Ola Bratteli,Derek W. Robinson
Limited preview
Operator Algebras and Quantum Statistical Mechanics: Equilibrium states ...
Operator Algebras and Quantum Statistical Mechanics: Equilibrium states ...
Ola Bratteli,Derek W. Robinson
Snippet view - 1981
Operator algebras and quantum statistical mechanics: C*- and W*-algebras ...
Operator algebras and quantum statistical mechanics: C*- and W*-algebras ...
Ola Bratteli,Derek W. Robinson
Snippet view - 1987
View all »

Common terms and phrases

Araki argument assume asymptotic abelianness automorphism group Bogoliubov Bogoliubov transformations Bose gas bounded C*-algebra C*-dynamical system CCR algebra classical commutation compact convergence convex Corollary corresponding decomposition defined denote dense density matrices derived Dirichlet boundary conditions dynamics eigenvalues elements energy equilibrium ergodic established Example exists external field Fermi ferromagnetic finite finite-volume Fock space function Gibbs condition Green's functions ground group of automorphisms Hamiltonian hence Hilbert space identity implies inequality integral interaction Ising model KMS condition lattice Lemma linear magnetization Math matrix measure modular Moreover Neumann algebra norm Notes and Remarks Observation one-parameter group particles perturbation Phys positive proof of Theorem properties Proposition prove quantum spin quantum spin systems quasi-free reduced density matrices relation representation result satisfies Section selfadjoint selfadjoint operator stability statistical mechanics subalgebra subset subspace symmetry t-invariant t-KMS temperature theory thermodynamic limit topology translationally invariant unique vector zero

References to this book

From other books

Selected Papers of M. Ohya
Selected Papers of M. Ohya
Masanori Ōya
No preview available - 2008
Spinors in Hilbert Space
Spinors in Hilbert Space
Roger Plymen,Paul Robinson
Limited preview - 1994
All Book Search results »

From Google Scholar

Semigroups of linear operators and applications
Jerome A Goldstein
Quantum groups and noncommutative geometry
Shahn Majid - 2000 - Journal of Mathematical Physics
The Non-Commutative Geometry of the Quantum Hall Effect
J Bellissard, A van Elst, H Schulz-Baldes - 1994 - Arxiv preprint cond-mat/9411052
An Introduction to Noncommutative Spaces and their Geometry
Giovanni Landi - 1997 - Arxiv preprint hep-th/9701078
All Scholar search results »

References from web pages

O.Bratteli
Office Address: Prof. Ola Bratteli Matematisk Institutt Universitetet i Oslo PB 1053 - Blindern N-0316 Oslo Norway; Phone: Office: +47-22 85 58 95 Fax(Dept. ...
www.math.uio.no/ ~bratteli/

Operator Methods in Quantum Mechanics Martin Schechter Dover ...
Название Operator Algebras and Quantum Statistical Mechanics 2 / Equilibrium States. Models in Quantum Statistical Mechanics ...
www.logobook.ru/ prod_show.php?object_uid=11167816

Nourrigat: Exponential of a hamiltonian in large subsets of a ...
[9] O. BRATTELI, dw ROBINSON, Operator algebras and quantum statistical mechanics. 2. Equilibrium states. Models in quantum statistical mechanics. ...
jedp.cedram.org/ jedp-bin/ fitem?id=JEDP_2005____A9_0

Phys. Rev. E 66, 016135 (2002): Ogata - Nonequilibrium properties ...
Nonequilibrium properties in the transverse XX chain. Yoshiko Ogata*; Department of Physics, Graduate School of Science, University of Tokyo, Hongo, 7-3-1, ...
link.aps.org/ doi/ 10.1103/ PhysRevE.66.016135

Fannes, Nachtergaele, Werner: Entropy estimates for finitely ...
Recherche et téléchargement d’archives de revues mathématiques numérisées. Accueil · Collections · Rechercher un article · A propos · Boîte à outils ...
www.numdam.org/ numdam-bin/ fitem?id=AIHPA_1992__57_3_259_0

Bibliographic information

QR code for Operator Algebras and Quantum Statistical Mechanics 2
TitleOperator Algebras and Quantum Statistical Mechanics 2: Equilibrium States. Models in Quantum Statistical Mechanics, Volume 2
Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States. Models in Quantum Statistical Mechanics, Derek W. Robinson
Volume 2 of Operator Algebras and Quantum Statistical Mechanics, Derek W. Robinson
Physics and Astronomy Online Library
Texts and monographs in physics, ISSN 0172-5998
Theoretical and Mathematical Physics
AuthorOla Bratteli
ContributorDerek W. Robinson
Edition2, revised
PublisherSpringer, 1997
ISBN3540614435, 9783540614432
Length517 pages
Subjects ›  › 

Mathematics / Group Theory
Science / Physics / General
Science / Physics / Mathematical & Computational
  
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