Quantum Probability For Probabilists

Author : Paul-Andre Meyer
Publisher : Springer
Page : 301 pages
File Size : 44,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662215586

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Quantum Probability for Probabilists by Paul-Andre Meyer Pdf

These notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability" , the main topic is "Quantum Stochastic Calculus" , a field which has recently got official recognition as 81825 in the Math.

Author : Paul André Meyer
Publisher : Springer
Page : 287 pages
File Size : 47,7 Mb
Release : 1993
Category : Distribution (Probability theory).
ISBN : 3540564764

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Quantum Probability for Probabilists by Paul André Meyer Pdf

In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide anintroduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis.

Author : R. L. Hudson,J. M. Lindsay
Publisher : World Scientific
Page : 376 pages
File Size : 48,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9810235410

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Quantum Probability Communications by R. L. Hudson,J. M. Lindsay Pdf

Much has changed in the world of quantum probability since the publication of the last volume in this series. Giants in the field, such as P-A Meyer, K R Parthasarathy and W von Waldenfels, have reached the age of retirement. Readers will, however, be pleased to see evidence in the present volume that Partha remains as creatively active as ever. The field itself, regarded at one time as the esoteric province of a small group of devotees, has come of age. It has attracted the enthusiastic commitment of an ever-growing army of young mathematicians and physicists, many of whom are represented here.

Author : Stéphane Attal
Publisher : Springer Science & Business
Page : 318 pages
File Size : 42,5 Mb
Release : 2003
Category : Mathematics
ISBN : 981238975X

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Quantum Probability Communications by Stéphane Attal Pdf

Extensions of quantum stochastic calculus / Stéphane Attal -- Quantum Itô algebras: axioms, representations, decompositions / Viacheslav Belavkin -- Free probability for probabilists / Philippe Biane -- Conditional expectations on von Neumann algebras / Carlo Cecchini -- Classical probability theory: an outline of stochastic integrals and diffusions / Michel Émery -- Quantum stochastic differential equations / Franco Fagnola -- Canonical commutation and anticommutation relations / Mark Fannes -- Quantum and classical stochastic calculus / Alexander Holevo -- An introduction to quantum stochastic calculus and some of its applications / Robin Hudson -- Stationary processes in quantum probability / Burkhard Kümmerer

Author : Stanley P. Gudder
Publisher : Academic Press
Page : 331 pages
File Size : 44,8 Mb
Release : 2014-06-28
Category : Science
ISBN : 9780080918488

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Quantum Probability by Stanley P. Gudder Pdf

Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism. Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles. The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.

Author : L Accardi
Publisher : World Scientific
Page : 420 pages
File Size : 47,8 Mb
Release : 1994-12-16
Category : Science
ISBN : 9789814501309

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Quantum Probability and Related Topics by L Accardi Pdf

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. Contents:On the Stochastic Limit of Quantum Chromodynamics (L Accardi et al.)Flows and Imprimitivity Systems (L Accardi et al.)Fermion Stochastic Flows on Quantum Algebras (D Applebaum)Examples of Unbounded Generators Leading to Nonconservative Minimal Semigroups (B V R Bhat & K B Sinha)On the Structure of Quantum Markov Processes (C Cecchini)Diffusion Processes in Fock Space (F Fagnola)On the Isomorphism of Poisson Space and Symmetric Fock Space (V Liebscher)Non-Linear Master Equation and Non-Crossing Cumulants (P Neu & R Speicher)A General Central Limit Theorem and Invariance Principle (R Speicher & W von Waldenfels)and other papers Readership: Mathematicians and mathematical physicists. keywords:Quantum Probability;Classical Probability;Quantum Algebras;Quantum Markov Processes;Fock Space;Mathematical Physics;White Noise

Author : Andrei Khrennikov,Bourama Toni
Publisher : Springer
Page : 295 pages
File Size : 40,7 Mb
Release : 2018-06-13
Category : Science
ISBN : 9783319749716

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Quantum Foundations, Probability and Information by Andrei Khrennikov,Bourama Toni Pdf

Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory. Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.

Author : Luigi Accardi,Wilhelm v. Waldenfels
Publisher : Springer
Page : 425 pages
File Size : 45,8 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540463115

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Quantum Probability and Applications V by Luigi Accardi,Wilhelm v. Waldenfels Pdf

These proceedings of the workshop on quantum probability held in Heidelberg, September 26-30, 1988 contains a representative selection of research articles on quantum stochastic processes, quantum stochastic calculus, quantum noise, geometry, quantum probability, quantum central limit theorems and quantum statistical mechanics.

Author : Luigi Accardi,Wilhelm v. Waldenfels
Publisher : Springer
Page : 541 pages
File Size : 55,9 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540395706

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Quantum Probability and Applications II by Luigi Accardi,Wilhelm v. Waldenfels Pdf

Author : S Attal,J. M Lindsay
Publisher : World Scientific
Page : 314 pages
File Size : 53,7 Mb
Release : 2003
Category : Science
ISBN : 9789812389756

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Quantum Probability Communications by S Attal,J. M Lindsay Pdf

Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12.

Author : S Attal,J M Lindsay
Publisher : World Scientific
Page : 604 pages
File Size : 42,6 Mb
Release : 2003-06-27
Category : Science
ISBN : 9789814485593

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Quantum Probability Communications by S Attal,J M Lindsay Pdf

0Keywords:Mathematics;Mathematical Physics;Quantum Probability;Stochastic Calculus;Noncommutative Probability;Free Probability

Author : R L Hudson,J Martin Lindsay
Publisher : World Scientific
Page : 372 pages
File Size : 49,6 Mb
Release : 1998-10-07
Category : Science
ISBN : 9789814495882

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Quantum Probability Communications: Volume X by R L Hudson,J Martin Lindsay Pdf

Much has changed in the world of quantum probability since the publication of the last volume in this series. Giants in the field, such as P-A Meyer, K R Parthasarathy and W von Waldenfels, have reached the age of retirement. Readers will, however, be pleased to see evidence in the present volume that Partha remains as creatively active as ever. The field itself, regarded at one time as the esoteric province of a small group of devotees, has come of age. It has attracted the enthusiastic commitment of an ever-growing army of young mathematicians and physicists, many of whom are represented here.

Author : J. M Lindsay
Publisher : World Scientific
Page : 294 pages
File Size : 40,5 Mb
Release : 2003
Category : Science
ISBN : 9789812389596

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Quantum Probability Communications Qp-Pq by J. M Lindsay Pdf

Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12.

Author : Luigi Accardi,Wolfgang Freudenberg,Michael Schurmann
Publisher : World Scientific
Page : 392 pages
File Size : 43,5 Mb
Release : 2007-07-12
Category : Mathematics
ISBN : 9789814474795

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Quantum Probability And Infinite Dimensional Analysis - Proceedings Of The 26th Conference by Luigi Accardi,Wolfgang Freudenberg,Michael Schurmann Pdf

This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability, 'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity illustrates that research in quantum probability and infinite dimensional analysis is very active and strongly involved in modern mathematical developments and applications.

Author : Michael Schürmann,Uwe Franz
Publisher : World Scientific
Page : 548 pages
File Size : 42,8 Mb
Release : 2005-01-12
Category : Science
ISBN : 9789814481021

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Quantum Probability and Infinite Dimensional Analysis by Michael Schürmann,Uwe Franz Pdf

This volume collects research papers in quantum probability and related fields and reflects the recent developments in quantum probability ranging from the foundations to its applications. Contents:Probability Measures in Terms of Creation, Annihilation and Neutral Operators (L Accardi et al.)Generating Function Method for Orthogonal Polynomials and Jacobi–Szegö Parameters (N Asai et al.)Multiquantum Markov Semigroups, Interacting Branching Processes and Nonlinear Kinetic Equations. Finite Dimensional Case (V P Belavkin & C R Williams)A Note on Vacuum-Adapted Semimartingales and Monotone Independence (A C R Belton)Regular Quantum Stochastic Cocycles have Exponential Product Systems (B V R Bhat & J M Lindsay)Quantum Mechanics on the Circle Through Hopf q-Deformations of the Kinematical Algebra with Possible Applications to Lévy Processes (V K Dobrev et al.)On Algebraic and Quantum Random Walks (D Ellinas)Dual Representations for the Schrödinger Algebra (P Feinsilver & R Schott)A Limit Theorem for Conditionally Independent Beam Splittings (K H Fichtner et al.)On Quantum Logical Gates on a General Fock Space (W Freudenberg et al.)On an Argument of David Deutsch (R Gill)The Method of Double Product Integrals in Quantisation of Lie Bialgebras (R L Hudson)Asymptotics of Large Truncated Haar Unitary Matrices (J L Réffy)Three Ways to Representations of BA(E) (M Skeide)On Topological Entropy of Quotients and Extensions (J Zacharias)and other papers Readership: Researchers in the fields of probability, mathematical physics and functional analysis. Keywords:Quantum Probability;Infinite Dimensional Analysis;Mathematical Physics;Lévy Processes;Interacting Fock Space;Quantum Markov ProcessesKey Features:Reflects recent developments in the fieldsAll the articles are contributed by renowned researchers