Quantum Probability Related Topics

Quantum Probability and Related Topics is a series of volumes based on material discussed at the various QP conferences. It aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis.

This volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory. This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications. Tools and techniques presented here will be of great value to researchers.

This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the ?-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed.

This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians. Contents:Existence of the Fock Representation for Current Algebras of the Galilei Algebra (L Accardi et al.)Modular Structures and Landau Levels (F Bagarello)On Spectral Approach to Pascal White Noise Functionals (A Barhoumi et al.)Spectral Analysis for Twisted Waveguides (P Briet)On the Classification of Invarient State of Generic Quantum Markov Semigroups: The Gaussian Gauge Invariant Case (S Hachicha)On Difficulties Appearing in the Study of Stochastic Volterra Equations (A Karczewska)Entanglement Protection and Generation in a Two-Atom System (M Orszag)Hilbert Molecules — Square Roots of Positive Maps (M Skeide)Multiparameter Quantum Stochastic Processes (W J Spring)and other papers Readership: Researchers in mathematical physics, stochastic analysis and probability and statistics. Keywords:Quantum Probability;Quantum Markov Semigroups;Entanglement;Quantum Information;Quantum Statistics;Quantum Dilations;Quantum Measurements;Non-Markovian Open Systems

This volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory.This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications.Tools and techniques presented here will be of great value to resear.

This volume contains recent results in quantum probability and related topics. The contributions include peer-reviewed papers on interacting Fock space and orthogonal polynomials, quantum Markov semigroups, infinitely divisible processes, free probability, white noise, quantum filtering and control, quantum information, dilations, applications of quantum probability in physics, and quantum and classical models in biology. This diversity reflects the strong and constructive relations between quantum probability and different sectors of mathematics, physics, and other sciences and technologies.

Quantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.

This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.