Contemporary Mathematics 2003; 328 pp; softcover Volume: 335 ISBN10: 0821832158 ISBN13: 9780821832158 List Price: US$92 Member Price: US$73.60 Order Code: CONM/335
 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. 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  W. Arveson  Four lectures on noncommutative dynamics
 R. T. Powers  Construction of \(E_0\)semigroups of \(\mathfrak B(\mathfrak h)\) from \(CP\)flows
 B. V. R. Bhat  Atomic dilations
 F. Cipriani and J.L. Sauvageot  Strong solutions to the Dirichlet problem for differential forms: A quantum dynamical semigroup approach
 D. E. Evans and P. R. Pinto  Modular invariants and their fusion rules
 R. Floricel  A decomposition of \(E_0\)semigroups
 R. Gohm  A duality between extension and dilation
 I. Hirshberg and J. Zacharias  On the structure of spectral algebras and their generalizations
 Y. Katayama and M. Takesaki  Outer actions of a countable discrete amenable group on an AFD factor
 T. Katsura  A construction of \(C^*\)algebras from \(C^*\)correspondences
 Y. Kawahigashi  Classification of operator algebraic conformal field theories
 A. Kishimoto  Rohlin property for flows
 C. Köstler  Survey on a quantum stochastic extension of Stone's theorem
 D. Markiewicz  Quantized convolution semigroups
 P. S. Muhly and B. Solel  A model for quantum Markov semigroups
 T. Oikhberg, H. P. Rosenthal, and E. Størmer  A predual characterization of semifinite von Neumann algebras
 S. Sakai  Pure states on \(C^*\)algebras
 M. Skeide  Commutants of von Neumann modules, representations of \(\mathcal{B}^a(E)\) and other topics related to product systems of Hilbert modules
 R. Speicher  Noncommutative Brownian motions
 B. Tsirelson  Nonisomorphic product systems
