Quantum Probability for Probabilists

Quantum Probability for Probabilists
Title Quantum Probability for Probabilists PDF eBook
Author Paul-Andre Meyer
Publisher Springer
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.

Quantum Probability Communications

Quantum Probability Communications
Title Quantum Probability Communications PDF eBook
Author R. L. Hudson
Publisher World Scientific
Pages 376
Release 1998
Genre Mathematics
ISBN 9789810235413

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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.

Quantum Probability

Quantum Probability
Title Quantum Probability PDF eBook
Author Stanley Gudder
Publisher Academic Press
Pages 344
Release 1988-08-28
Genre Mathematics
ISBN

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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.

Probabilities on the Heisenberg Group

Probabilities on the Heisenberg Group
Title Probabilities on the Heisenberg Group PDF eBook
Author Daniel Neuenschwander
Publisher Springer
Pages 146
Release 2006-11-14
Genre Mathematics
ISBN 3540685901

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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.

Partial Differential Equations for Probabilists

Partial Differential Equations for Probabilists
Title Partial Differential Equations for Probabilists PDF eBook
Author Daniel W. Stroock
Publisher Cambridge University Press
Pages 216
Release 2008-04-28
Genre Mathematics
ISBN 0521886511

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Kolmogorov's forward, basic results -- Non-elliptic regularity results -- Preliminary elliptic regularity results -- Nash theory -- Localization -- On a manifold -- Subelliptic estimates and Hörmander's theorem.

Quantum Probability for Probabilists

Quantum Probability for Probabilists
Title Quantum Probability for Probabilists PDF eBook
Author Paul André Meyer
Publisher
Pages
Release 1995
Genre Probabilities
ISBN 9780803278226

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The Theory of Quantum Information

The Theory of Quantum Information
Title The Theory of Quantum Information PDF eBook
Author John Watrous
Publisher
Pages 599
Release 2018-04-26
Genre Computers
ISBN 1107180562

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Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.