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Advances in Quantum Dynamics
 
Edited by: Geoffrey L. Price U.S. Naval Academy, Annapolis, MD
B. Mitchell Baker U.S. Naval Academy, Annapolis, MD
Palle E.T. Jorgensen University of Iowa, Iowa City, IA
Paul S. Muhly University of Iowa, Iowa City, IA
Advances in Quantum Dynamics
Softcover ISBN:  978-0-8218-3215-8
Product Code:  CONM/335
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7925-2
Product Code:  CONM/335.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3215-8
eBook: ISBN:  978-0-8218-7925-2
Product Code:  CONM/335.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Advances in Quantum Dynamics
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Advances in Quantum Dynamics
Edited by: Geoffrey L. Price U.S. Naval Academy, Annapolis, MD
B. Mitchell Baker U.S. Naval Academy, Annapolis, MD
Palle E.T. Jorgensen University of Iowa, Iowa City, IA
Paul S. Muhly University of Iowa, Iowa City, IA
Softcover ISBN:  978-0-8218-3215-8
Product Code:  CONM/335
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7925-2
Product Code:  CONM/335.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3215-8
eBook ISBN:  978-0-8218-7925-2
Product Code:  CONM/335.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3352003; 328 pp
    MSC: 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 one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversible systems, also called dissipative systems. The time parameter is the half-line, 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.

    Readership

    Graduate 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 CP-flows [ MR 2026011 ]
    • B. V. Rajarama Bhat — Atomic dilations [ MR 2026012 ]
    • Fabio Cipriani and Jean-Luc 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 semi-finite 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 — Non-commutative Brownian motions [ MR 2029631 ]
    • Boris Tsirelson — Non-isomorphic product systems [ MR 2029632 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3352003; 328 pp
MSC: 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 one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversible systems, also called dissipative systems. The time parameter is the half-line, 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.

Readership

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 CP-flows [ MR 2026011 ]
  • B. V. Rajarama Bhat — Atomic dilations [ MR 2026012 ]
  • Fabio Cipriani and Jean-Luc 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 semi-finite 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 — Non-commutative Brownian motions [ MR 2029631 ]
  • Boris Tsirelson — Non-isomorphic product systems [ MR 2029632 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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