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Softcover ISBN:  9780821832158 
Product Code:  CONM/335 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
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Product Code:  CONM/335.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821832158 
eBook ISBN:  9780821879252 
Product Code:  CONM/335.B 
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AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 335; 2003; 328 ppMSC: Primary 46; 47; 60
This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras.
Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems. Following the work of M. H. Stone, von Neumann, and others on the structure of oneparameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of timereversible dynamical systems. This book deals with the mathematics of timeirreversible systems, also called dissipative systems. The time parameter is the halfline, and the transformations are now endomorphisms as opposed to automorphisms.
For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such as Brownian motion, dilation theory, quantum probability, and free probability.
The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.
ReadershipGraduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.

Table of Contents

Articles

William Arveson — Four lectures on noncommutative dynamics [ MR 2026010 ]

Robert T. Powers — Construction of $E_0$semigroups of $\mathfrak {B}(\mathfrak {h})$ from CPflows [ MR 2026011 ]

B. V. Rajarama Bhat — Atomic dilations [ MR 2026012 ]

Fabio Cipriani and JeanLuc Sauvageot — Strong solutions to the Dirichlet problem for differential forms: a quantum dynamical semigroup approach [ MR 2026013 ]

David E. Evans and Paulo R. Pinto — Modular invariants and their fusion rules [ MR 2026014 ]

Remus Floricel — A decomposition of $E_0$semigroups [ MR 2026015 ]

Rolf Gohm — A duality between extension and dilation [ MR 2026016 ]

Ilan Hirshberg and Joachim Zacharias — On the structure of spectral algebras and their generalizations [ MR 2026017 ]

Yoshikazu Katayama and Masamichi Takesaki — Outer actions of a countable discrete amenable group on an AFD factor [ MR 2029621 ]

Takeshi Katsura — A construction of $C^*$algebras from $C^*$correspondences [ MR 2029622 ]

Yasuyuki Kawahigashi — Classification of operator algebraic conformal field theories [ MR 2029623 ]

Akitaka Kishimoto — Rohlin property for flows [ MR 2029624 ]

Claus Köstler — Survey on a quantum stochastic extension of Stone’s theorem [ MR 2029625 ]

Daniel Markiewicz — Quantized convolution semigroups [ MR 2029626 ]

Paul S. Muhly and Baruch Solel — A model for quantum Markov semigroups [ MR 2029627 ]

Timur Oikhberg, Haskell P. Rosenthal and Erling Størmer — A predual characterization of semifinite von Neumann algebras [ MR 2029628 ]

Shôichirô Sakai — Pure states on $C^*$algebras [ MR 2029629 ]

Michael Skeide — Commutants of von Neumann modules, representations of $\scr B^a(E)$ and other topics related to product systems of Hilbert modules [ MR 2029630 ]

Roland Speicher — Noncommutative Brownian motions [ MR 2029631 ]

Boris Tsirelson — Nonisomorphic product systems [ MR 2029632 ]


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This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras.
Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems. Following the work of M. H. Stone, von Neumann, and others on the structure of oneparameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of timereversible dynamical systems. This book deals with the mathematics of timeirreversible systems, also called dissipative systems. The time parameter is the halfline, and the transformations are now endomorphisms as opposed to automorphisms.
For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such as Brownian motion, dilation theory, quantum probability, and free probability.
The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.
Graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.

Articles

William Arveson — Four lectures on noncommutative dynamics [ MR 2026010 ]

Robert T. Powers — Construction of $E_0$semigroups of $\mathfrak {B}(\mathfrak {h})$ from CPflows [ MR 2026011 ]

B. V. Rajarama Bhat — Atomic dilations [ MR 2026012 ]

Fabio Cipriani and JeanLuc Sauvageot — Strong solutions to the Dirichlet problem for differential forms: a quantum dynamical semigroup approach [ MR 2026013 ]

David E. Evans and Paulo R. Pinto — Modular invariants and their fusion rules [ MR 2026014 ]

Remus Floricel — A decomposition of $E_0$semigroups [ MR 2026015 ]

Rolf Gohm — A duality between extension and dilation [ MR 2026016 ]

Ilan Hirshberg and Joachim Zacharias — On the structure of spectral algebras and their generalizations [ MR 2026017 ]

Yoshikazu Katayama and Masamichi Takesaki — Outer actions of a countable discrete amenable group on an AFD factor [ MR 2029621 ]

Takeshi Katsura — A construction of $C^*$algebras from $C^*$correspondences [ MR 2029622 ]

Yasuyuki Kawahigashi — Classification of operator algebraic conformal field theories [ MR 2029623 ]

Akitaka Kishimoto — Rohlin property for flows [ MR 2029624 ]

Claus Köstler — Survey on a quantum stochastic extension of Stone’s theorem [ MR 2029625 ]

Daniel Markiewicz — Quantized convolution semigroups [ MR 2029626 ]

Paul S. Muhly and Baruch Solel — A model for quantum Markov semigroups [ MR 2029627 ]

Timur Oikhberg, Haskell P. Rosenthal and Erling Størmer — A predual characterization of semifinite von Neumann algebras [ MR 2029628 ]

Shôichirô Sakai — Pure states on $C^*$algebras [ MR 2029629 ]

Michael Skeide — Commutants of von Neumann modules, representations of $\scr B^a(E)$ and other topics related to product systems of Hilbert modules [ MR 2029630 ]

Roland Speicher — Noncommutative Brownian motions [ MR 2029631 ]

Boris Tsirelson — Nonisomorphic product systems [ MR 2029632 ]