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| Author | : Paul-Andre Meyer |
| Publisher | : Springer |
| Total Pages | : 301 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 3662215586 |
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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 |
| Total Pages | : 287 |
| Release | : 1993 |
| Genre | : Distribution (Probability theory). |
| ISBN | : 9783540564768 |
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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 | : Paul A. Meyer |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662199992 |
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| Author | : R. L. Hudson |
| Publisher | : World Scientific |
| Total Pages | : 376 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9789810235413 |
Download Quantum Probability Communications Book in PDF, ePub and Kindle
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 | : Stanley P. Gudder |
| Publisher | : Academic Press |
| Total Pages | : 331 |
| Release | : 2014-06-28 |
| Genre | : Science |
| ISBN | : 0080918484 |
Download Quantum Probability Book in PDF, ePub and Kindle
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 | : Stéphane Attal |
| Publisher | : Springer Science & Business |
| Total Pages | : 318 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9789812389756 |
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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 | : Andrei Khrennikov |
| Publisher | : Springer |
| Total Pages | : 295 |
| Release | : 2018-06-13 |
| Genre | : Science |
| ISBN | : 3319749714 |
Download Quantum Foundations, Probability and Information Book in PDF, ePub and Kindle
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 | : Daniel Neuenschwander |
| Publisher | : Springer |
| Total Pages | : 146 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540685901 |
Download Probabilities on the Heisenberg Group Book in PDF, ePub and Kindle
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
| Author | : Luigi Accardi |
| Publisher | : Springer |
| Total Pages | : 425 |
| Release | : 2006-11-14 |
| Genre | : Science |
| ISBN | : 3540463119 |
Download Quantum Probability and Applications V Book in PDF, ePub and Kindle
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 | : S Attal |
| Publisher | : World Scientific |
| Total Pages | : 314 |
| Release | : 2003 |
| Genre | : Science |
| ISBN | : 981238975X |
Download Quantum Probability Communications Book in PDF, ePub and Kindle
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.
