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Author : Sergio Albeverio,Giulio Casati,D. Merlini
Publisher : Springer
Page : 572 pages
File Size : 53,7 Mb
Release : 1986
Category : Quantum systems
ISBN : UCAL:B4423159
Author : K.R. Parthasarathy
Publisher : Birkhäuser
Page : 299 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886413
"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.
Author : Rolando Rebolledo
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213727
The seminar on Stochastic Analysis and Mathematical Physics started in 1984 at the Catholic University of Chile in Santiago and has been an on going research activity. Since 1995, the group has organized international workshops as a way of promoting a broader dialogue among experts in the areas of classical and quantum stochastic analysis, mathematical physics and physics. This volume, consisting primarily of contributions to the Third Inter national Workshop on Stochastic Analysis and Mathematical Physics (in Spanish ANESTOC), held in Santiago, Chile, in October 1998, focuses on an analysis of quantum dynamics and related problems in probability the ory. Various articles investigate quantum dynamical semigroups and new results on q-deformed oscillator algebras, while others examine the appli cation of classical stochastic processes in quantum modeling. As in previous workshops, the topic of quantum flows and semigroups occupied an important place. In her paper, R. Carbone uses a spectral type analysis to obtain exponential rates of convergence towards the equilibrium of a quantum dynamical semigroup in the £2 sense. The method is illus trated with a quantum extension of a classical birth and death process. Quantum extensions of classical Markov processes lead to subtle problems of domains. This is in particular illustrated by F. Fagnola, who presents a pathological example of a semigroup for which the largest * -subalgebra (of the von Neumann algebra of bounded linear operators of £2 (lR+, IC)), con tained in the domain of its infinitesimal generator, is not a-weakly dense.
Author : David Applebaum,B.V. Rajarama Bhat,Johan Kustermans,J. Martin Lindsay
Publisher : Springer
Page : 299 pages
File Size : 46,5 Mb
Release : 2005-09-14
Category : Mathematics
ISBN : 9783540314509
This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,7 Mb
Release : 2024-05-12
Category : Electronic
ISBN : 9789814479172
Author : Masao Nagasawa
Publisher : Birkhäuser
Page : 609 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883832
From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry." ZAA
Author : Giulio Casati,J. Ford
Publisher : Unknown
Page : 388 pages
File Size : 40,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366218365X
Author : Ana Isabel Cardoso,Margarida de Faria,Jürgen Potthoff,Roland Sénéor,L. Streit
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401102193
Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993
Author : Stanley P. Gudder
Publisher : Courier Corporation
Page : 242 pages
File Size : 49,7 Mb
Release : 2014-05-05
Category : Science
ISBN : 9780486149189
This introductory survey of stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering also serves as a useful and comprehensive reference volume. 1979 edition.
Author : Kalyan B. Sinha,Debashish Goswami
Publisher : Cambridge University Press
Page : 301 pages
File Size : 52,5 Mb
Release : 2007-01-25
Category : Mathematics
ISBN : 9781139461696
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
Author : Yuri E. Gliklikh
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 49,7 Mb
Release : 2010-12-07
Category : Mathematics
ISBN : 0857291637
Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.
Author : Takeyuki Hida
Publisher : Unknown
Page : 300 pages
File Size : 50,6 Mb
Release : 2005
Category : Probabilities
ISBN : 9812565264
Author : Rolando Rebolledo
Publisher : Birkhäuser
Page : 172 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880183
The seminar on Stochastic Analysis and Mathematical Physics of the Ca tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physics, and physics. This volume collects most of the contributions to the Fourth Interna tional Workshop on Stochastic Analysis and Mathematical Physics (whose Spanish abbreviation is "ANESTOC"; in English, "STAMP"), held in San tiago, Chile, from January 5 to 11, 2000. The workshop style stimulated a vivid exchange of ideas which finally led to a number of written con tributions which I am glad to introduce here. However, we are currently submitted to a sort of invasion of proceedings books, and we do not want to increase our own shelves with a new one of the like. On the other hand, the editors of conference proceedings have to use different exhausting and com pulsive strategies to persuade authors to write and provide texts in time, a task which terrifies us. As a result, this volume is aimed at smoothly start ing a new kind of publication. What we would like to have is a collection of books organized like our seminar.
Author : A.B. Cruzeiro,J.-C. Zambrini
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201274
This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.
Author : Harish Parthasarathy
Publisher : CRC Press
Page : 490 pages
File Size : 44,6 Mb
Release : 2021-06-24
Category : Mathematics
ISBN : 9781000425932
This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. The problems are chosen to motivate the interested reader to learn more about these subjects from other standard sources. Stochastic Process theory is applied to the study of differential equations of mechanics subject to external noise. Some issues in general relativity like Geodesic motion, field theory in curved space time etc. are discussed via isolated problems. The more recent quantum stochastic process theory as formulated by R.L. Hudson and K. R. Parathasarathy is discussed. This provides a non commutative operator theoretic version of stochastic process theory. V.P. Belavkin's approach to quantum filtering based on non demolition measurements and Hudson Parathasarathy calculus has been discussed in detail. Quantum versions of the simple exclusion model in Markov process theory have been included. 3D Robots carring a current density interacting with an external Klein- Gordon or Electromagnetic field has been given some attention. The readers will after going through this book, be ready to carry out independent research in classical and quantum field theory and stochastic processes as applied to practical problems. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.