Stochastic Methods And Computer Techniques In Quantum Dynamics

Author : H. Mitter,L. Pittner
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783709187807

Get Book

Stochastic Methods and Computer Techniques in Quantum Dynamics by H. Mitter,L. Pittner Pdf

This volume contains the written versions of lectures held at the "23. Internationale Universit~tswochen fUr Kernphysik" in Schladming, Austria, in February 1984. Once again the generous support of our sponsors, the Austrian Ministry of Science and Research, the Styrian Government and others, had made it possible to organize this school. The aim of the topics chosen for the meeting was to present different aspects of stochastic methods and techniques. These methods have opened up new ways to attack problems in a broad field ranging from quantum mechanics to quantum field theory. Thanks to the efforts of the lecturers it was possible to take this development into account and show relations to areas where stochastic methods have been used for a long time. Due to limited space only short manuscript versions of the many seminars presented could be included. The lecture notes were reexamined by the authors after the school and are now published in their final form. It is a pleasure to thank all the lecturers for their efforts which made it possible to speed up publication. Thanks are also due to Mrs. Neuhold for her careful typing of the notes. H. Mitter L. Pittner Acta Physica Austriaca, Suppl. XXVI, 3-52 (1984) © by Springer-Verlag 1984 STOCHASTIC PROCESSES - QUANTUM PHYSICS+ by L. STREIT Universitat Bielefeld BiBoS D-4800 Bielefeld. FR Germany I.

Author : Stanley P. Gudder
Publisher : Courier Corporation
Page : 242 pages
File Size : 43,6 Mb
Release : 2014-05-05
Category : Science
ISBN : 9780486149189

Get Book

Stochastic Methods in Quantum Mechanics by Stanley P. Gudder Pdf

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 : Masao Nagasawa
Publisher : Birkhäuser
Page : 609 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883832

Get Book

Stochastic Processes in Quantum Physics by Masao Nagasawa Pdf

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 : Stanley Gudder
Publisher : Unknown
Page : 219 pages
File Size : 52,9 Mb
Release : 2014-01-01
Category : Quantum theory
ISBN : 1306862388

Get Book

Stochastic Methods in Quantum Mechanics by Stanley Gudder Pdf

Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory. The text assumes a basic knowledge of functional analysis; although some experience with probability theory and quantum mechanics is helpful, necessary ideas and results from these two disciplines are developed as needed. A selection of exercises follows each chapter, and proofs to most of the theorems are included. A comprehensive bibliography allows researchers and students to continue in the direction of their individual interests.

Author : Baez John C,Biamonte Jacob D
Publisher : World Scientific
Page : 276 pages
File Size : 53,5 Mb
Release : 2018-02-14
Category : Science
ISBN : 9789813226968

Get Book

Quantum Techniques In Stochastic Mechanics by Baez John C,Biamonte Jacob D Pdf

We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets. Contents: Stochastic Petri Nets The Rate Equation The Master Equation Probabilities vs Amplitudes Annihilation and Creation Operators An Example from Population Biology Feynman Diagrams The Anderson–Craciun–Kurtz Theorem An Example of the Anderson–Craciun–Kurtz Theorem A Stochastic Version of Noether's Theorem Quantum Mechanics vs Stochastic Mechanics Noether's Theorem: Quantum vs Stochastic Chemistry and the Desargues Graph Graph Laplacians Dirichlet Operators and Electrical Circuits Perron–Frobenius Theory The Deficiency Zero Theorem Example of the Deficiency Zero Theorem Example of the Anderson–Craciun–Kurtz Theorem The Deficiency of a Reaction Network Rewriting the Rate Equation The Rate Equation and Markov Processes Proof of the Deficiency Zero Theorem Noether's Theorem for Dirichlet Operators Computation and Petri Nets Summary Table Readership: Graduate students and researchers in the field of quantum and mathematical physics. Keywords: Stochastic;Quantum;Markov Process;Chemical Reaction Network;Petri NetReview: Key Features: It's a light-hearted introduction to a deep analogy between probability theory and quantum theory It explains how stochastic Petri nets can be used in modeling in biology, chemistry, and many other fields It gives new proofs of some fundamental theorems about chemical reaction networks

Author : Robert E. Wyatt
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 46,8 Mb
Release : 2006-05-28
Category : Mathematics
ISBN : 9780387281452

Get Book

Quantum Dynamics with Trajectories by Robert E. Wyatt Pdf

This is a rapidly developing field to which the author is a leading contributor New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book Useful to both students and researchers

Author : Mikio Namiki
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 53,8 Mb
Release : 2008-10-04
Category : Science
ISBN : 9783540472179

Get Book

Stochastic Quantization by Mikio Namiki Pdf

This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. S. Wu in 1981 and then developed by many workers. I assume that the reader has finished a standard course in quantum field theory. The Parisi-Wu stochastic quantization method gives quantum mechanics as the thermal-equilibrium limit of a hypothetical stochastic process with respect to some fictitious time other than ordinary time. We can consider this to be a third method of quantization; remarkably different from the conventional theories, i. e, the canonical and path-integral ones. Over the past ten years, we have seen the technical merits of this method in quantizing gauge fields and in performing large numerical simulations, which have never been obtained by the other methods. I believe that the stochastic quantization method has the potential to extend the territory of quantum mechanics and of quantum field theory. However, I should remark that stochastic quantization is still under development through many mathematical improvements and physical applications, and also that the fictitious time of the theory is only a mathematical tool, for which we do not yet know its origin in the physical background. For these reasons, in this book, I attempt to describe its theoretical formulation in detail as well as practical achievements.

Author : K.H. Namsrai
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400945180

Get Book

Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics by K.H. Namsrai Pdf

over this stochastic space-time leads to the non local fields considered by G. V. Efimov. In other words, stochasticity of space-time (after being averaged on a large scale) as a self-memory makes the theory nonlocal. This allows one to consider in a unified way the effect of stochasticity (or nonlocality) in all physical processes. Moreover, the universal character of this hypothesis of space-time at small distances enables us to re-interpret the dynamics of stochastic particles and to study some important problems of the theory of stochastic processes [such as the relativistic description of diffusion, Feynman type processes, and the problem of the origin of self-turbulence in the motion of free particles within nonlinear (stochastic) mechanics]. In this direction our approach (Part II) may be useful in recent developments of the stochastic interpretation of quantum mechanics and fields due to E. Nelson, D. Kershaw, I. Fenyes, F. Guerra, de la Pena-Auerbach, J. -P. Vigier, M. Davidson, and others. In particular, as shown by N. Cufaro Petroni and J. -P. Vigier, within the discussed approach, a causal action-at-distance interpretation of a series of experiments by A. Aspect and his co-workers indicating a possible non locality property of quantum mechanics, may also be obtained. Aspect's results have recently inspired a great interest in different nonlocal theories and models devoted to an understanding of the implications of this nonlocality. This book consists of two parts.

Author : Sergio Albeverio,Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 50,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0821819593

Get Book

Stochastic Processes, Physics and Geometry: New Interplays. I by Sergio Albeverio,Fritz Gesztesy Pdf

This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.

Author : Sergio Albeverio,Raphael Höegh-Krohn
Publisher : Cambridge University Press
Page : 568 pages
File Size : 53,6 Mb
Release : 1992-06-26
Category : Mathematics
ISBN : 0521419301

Get Book

Ideas and Methods in Quantum and Statistical Physics: Volume 2 by Sergio Albeverio,Raphael Höegh-Krohn Pdf

A collection of essays by many of the closest co-workers of Raphael Høegh-Krohn.

Author : Luigi Accardi,Wilhelm v. Waldenfels
Publisher : Springer
Page : 541 pages
File Size : 42,7 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540395706

Get Book

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

Author : Sonia Mazzucchi
Publisher : World Scientific
Page : 225 pages
File Size : 49,8 Mb
Release : 2009
Category : Science
ISBN : 9789812836908

Get Book

Mathematical Feynman Path Integrals and Their Applications by Sonia Mazzucchi Pdf

Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman's ideas. This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author. Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.

Author : Ana Isabel Cardoso,Margarida de Faria,Jürgen Potthoff,Roland Sénéor,L. Streit
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401102193

Get Book

Stochastic Analysis and Applications in Physics by Ana Isabel Cardoso,Margarida de Faria,Jürgen Potthoff,Roland Sénéor,L. Streit Pdf

Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993

Author : Kai Lai Chung,Jean-Claude Zambrini
Publisher : World Scientific
Page : 228 pages
File Size : 48,8 Mb
Release : 2003
Category : Science
ISBN : 9812384154

Get Book

Introduction to Random Time and Quantum Randomness by Kai Lai Chung,Jean-Claude Zambrini Pdf

This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown. In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.

Author : Ian M Davies,Aubrey Truman
Publisher : World Scientific
Page : 326 pages
File Size : 41,9 Mb
Release : 1992-05-30
Category : Electronic
ISBN : 9789814554732

Get Book

Stochastics And Quantum Mechanics by Ian M Davies,Aubrey Truman Pdf

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.