WORLD SCIENTIFIC eBooks

Stochastics and quantum mechanics : Swansea, Summer 1990

Aubrey Truman, Ian M Davies

Published Jan 1, 1992• 2 citations

Abstract

"This volume contains papers which were presented at a series of short meetings collectively entitled "Stochastics and Quantum Mechanics" held in Swansea over the summer of 1990. Also included are some papers not presented at the meetings, but in the same subject area, authored by attendees or their co-workers. The topics covered include diffusion processes, stochastic mechanics, statistical mechanics, large deviations and Wiener-Hopf theory. The papers are in the main immediately accessible to workers in the field and provide a reasonable coverage of current areas of interest centering around uses of probabilistic methods in mathematical physics."--Publisher's website

DOI: 10.1142/1696#t=toc

Related papers

Stochastic analysis and mathematical physics (SAMP/ANESTOC 2002) : proceedings of the Mathematical Legacy of R P Feynman, Lisbon, Portugal, 3 - 7, June 2002, proceedings of the Open Systems and Quantum Statistical Mechanics, Santiago, Chile, 7 - 11, January 2002

Rolando Rebollendo, Jorge Rezende, Jean-Claude Zambrini

The book collects a series of papers centered on two main streams: Feynman path integral approach to Quantum Mechanics and statistical mechanics of quantum open systems. Key authors discuss the state-of-the-art within their fields of expertise. In addition, the volume includes a number of contributed papers with new results, which have been thoroughly refereed. The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focusing, in particular on Feynman functional integral approach and, on the other hand, in quantum probability. The book is addressed to an audience of mathematical physicists, as well as specialists in probability theory, stochastic analysis and operator algebras.

WORLD SCIENTIFIC eBooksJan 1, 20040 citations

Quantum groups, integrable models and statistical systems : 1992 CAP/NSERC Summer Institute in Theoretical Physics, Kingston, Ontario, Canada, 13-18 July 1992

Jean LeTourneux, Luc Vinet

This volume contains the lectures presented at the workshop entitled Quantum Groups, Integrable Models and Statistical Systems. The papers give either a full exposition of original results or a review of fundamental aspects of this active research area.

WORLD SCIENTIFIC eBooksJan 1, 19931 citation

Introduction and Summary

Mou-Hsiung Chang

It is widely known that the commutative probability theory based on Kolmogorov's measure theoretic axioms and the quantum probability theory based on von Neumann's postulates were both created at about the same time in the 1930s (see, e.g., Kolmogorov [Kol50] and von Neumann [vNeu55] for the origins of these 2 very different but parallel lines of theory). Following Kolmogorov's original work, theory of the classical Markov processes has been the subject of intensive research for the last few decades. The classical theory, its applications, and their connections to other areas of research have been systematically developed by many prominent probabilists as illuminated by their widely referenced monographs such as those of Dynkin [Dyn62], Blumenthal and Getoor [BG68], Ethier and Kurtz [EK85], Renuv and Yor [RY99], and others. On the other hand, development of a complete theory of quantum stochastics such as quantum Markov processes has been progressing at a much slower pace in comparison with that of its classical counterpart. This is perhaps because development of a theory of quantum stochastics and quantum Markov processes requires an unusually large number of tools from operator theory and perhaps also because the probabilistic and analytical tools for understanding sample path behaviors of quantum stochastic processes have yet to be developed. The main goal of this monograph is to give a systematic exploration of relevant topics in quantum Markov processes in hopes of stimulating further research along this line and of stimulating interest in the classical stochastics community for research in its quantum counterpart. This monograph is written largely based on the current account of relevant research results by widely surveying relevant results contributed by many prominent researchers in quantum probability, quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigroups, strong quantum Markov processes, and large time asymptotic behaviors of quantum Markov semigroups through a systematic and self-contained introduction/presentation of these very interesting topics in an attempt to illuminate the rigor and beauty of quantum stochastics and quantum Markov processes.

Cambridge University Press eBooksFeb 9, 20150 citations

Stochastic Processes in Quantum Physics

Masao Nagasawa

"Stochastic Processes in Quantum Physics" addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in pa

Birkhäuser Basel eBooksJan 1, 200075 citations

Scattering theory in mathematical physics : proceedings of the NATO Advanced Study Institute held at Denver, Colo.,U.S.A, June 11-29, 1973

James A. LaVita, Jean-Paul Marchand

These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled Scattering Theory in Mathematics and Physics held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.

D. Reidel eBooksJan 1, 19742 citations

Quantum mechanics : a stochastic approach

Ramabhadra Vasudevan, Kanniyappan Parthasarathy, Ravishankar Ramanathan

Preface / Forward / Acknowledgements / Introduction / Invitation to Stochastic Calculus / Hydrodynamical Formulation of Quantum Mechanics / Stochastic Diffusion Processes / Selected Problems in Stochastic Mechanics / Stochastic Variational Principles / Euclidean Quantum Mechanics / Stochastic Path Space Picture / Relativistic Stochastic Mechanics / Dirac Equation - Stochastic Viewpoint / Stochastic Field Theory / Stochastic Mechanics on Manifolds / Stochastic Route to Quantum Mechanics - Quest Continues / References / Author Index / Subject Index.

Jan 1, 20084 citations