Quantum Techniques In Stochastic Mechanics

Author : Baez John C,Biamonte Jacob D
Publisher : World Scientific
Page : 276 pages
File Size : 47,9 Mb
Release : 2018-02-14
Category : Science
ISBN : 9789813226968

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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 : Stanley P. Gudder
Publisher : Courier Corporation
Page : 242 pages
File Size : 47,9 Mb
Release : 2014-05-05
Category : Science
ISBN : 9780486149189

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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 : Stanley Gudder
Publisher : Unknown
Page : 219 pages
File Size : 42,7 Mb
Release : 2014-01-01
Category : Quantum theory
ISBN : 1306862388

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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 : Margaret Prugovecki
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400944923

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Stochastic Quantum Mechanics and Quantum Spacetime by Margaret Prugovecki Pdf

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

Author : Eduard Prugovečki
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 48,6 Mb
Release : 1984-01-31
Category : Gardening
ISBN : 902771617X

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Stochastic Quantum Mechanics and Quantum Spacetime by Eduard Prugovečki Pdf

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

Author : K.H. Namsrai
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400945180

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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 : Masao Nagasawa
Publisher : Birkhäuser
Page : 609 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883832

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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 : Ph. Blanchard,Ph. Combe,W. Zheng
Publisher : Unknown
Page : 184 pages
File Size : 48,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662136058

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Mathematical and Physical Aspects of Stochastic Mechanics by Ph. Blanchard,Ph. Combe,W. Zheng Pdf

Author : Ramabhadra Vasudevan,R. Ramanathan
Publisher : Alpha Science International, Limited
Page : 316 pages
File Size : 52,5 Mb
Release : 2008
Category : Science
ISBN : STANFORD:36105131736428

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Quantum Mechanics by Ramabhadra Vasudevan,R. Ramanathan Pdf

"One of the great debates albeit a schism in twentieth century physics arose over the interpretation of the quantum phenomenon. On the one hand was the so called 'Copenhagen School' with Neils Bohr as its high priest and on the other were the objective realists under the leadership of Albert Einstein. The former stressed the role of the nature of measurement as the source of the quantum phenomenon, while the latter attributed it to some underlying 'Objective cause'. The attempt of this book is to present a self consistent treatment of quantum phenomenon using one of the most promising 'Objective realist' approach, namely, the stochastic formulation of quantum mechanics which a whole school of physicists who were and are votaries to the objective realist world view, have tried to develop over the last several decades. There are many facets of this scheme that are rich areas for further pursuit by young and enthusiastic physicists, and this book, hopefully, will induce many to pursue this vision."--BOOK JACKET.

Author : Ian M Davies,Aubrey Truman
Publisher : World Scientific
Page : 326 pages
File Size : 48,9 Mb
Release : 1992-05-30
Category : Electronic
ISBN : 9789814554732

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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.

Author : Luigi Accardi,Yun Gang Lu,Igor Volovich
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 54,7 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662049297

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Quantum Theory and Its Stochastic Limit by Luigi Accardi,Yun Gang Lu,Igor Volovich Pdf

Well suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.

Author : H. Mitter,L. Pittner
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783709187807

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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 : Edward Nelson
Publisher : Princeton University Press
Page : 155 pages
File Size : 43,9 Mb
Release : 1985-05-21
Category : Science
ISBN : 9780691083797

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Quantum Fluctuations by Edward Nelson Pdf

Stochastic mechanics is a description of quantum phenomena in classical probabilistic terms. This work contains a detailed account of the kinematics of diffusion processes, including diffusions on curved manifolds which are necessary for the treatment of spin in stochastic mechanics. The dynamical equations of the theory are derived from a variational principle, and interference, the asymptotics of free motion, bound states, statistics, and spin are described in classical terms. In addition to developing the formal mathematical aspects of the theory, the book contains discussion of possible physical causes of quantum fluctuations in terms of an interaction with a background field. The author gives a critical analysis of stochastic mechanics as a candidate for a realistic theory of physical processes, discussing measurement, local causality in the sense of Bell, and the failure of the theory in its present form to satisfy locality.

Author : Folkert Kuipers
Publisher : Unknown
Page : 0 pages
File Size : 54,8 Mb
Release : 2023
Category : Electronic
ISBN : 3031314492

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Stochastic Mechanics by Folkert Kuipers Pdf

Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription. The book builds on recent developments in this theory, and shows that quantum mechanics can be unified with the theory of Brownian motion in a single mathematical framework. Moreover, it discusses the extension of the theory to curved spacetime using second order geometry, and the induced Itô deformations of the spacetime symmetries. The book is self-contained and provides an extensive review of stochastic mechanics of the single spinless particle. The book builds up the theory on a step by step basis. It starts, in chapter 2, with a review of the classical particle subjected to scalar and vector potentials. In chapter 3, the theory is extended to the study of a Brownian motion in any potential, by the introduction of a Gaussian noise. In chapter 4, the Gaussian noise is complexified. The result is a complex diffusion theory that contains both Brownian motion and quantum mechanics as a special limit. In chapters 5, the theory is extended to relativistic diffusion theories. In chapter 6, the theory is further generalized to the context of pseudo-Riemannian geometry. Finally, in chapter 7, some interpretational aspects of the stochastic theory are discussed in more detail. The appendices concisely review relevant notions from probability theory, stochastic processes, stochastic calculus, stochastic differential geometry and stochastic variational calculus. The book is aimed at graduate students and researchers in theoretical physics and applied mathematics with an interest in the foundations of quantum theory and Brownian motion. The book can be used as reference material for courses on and further research in stochastic mechanics, stochastic quantization, diffusion theories on curved spacetimes and quantum gravity.

Author : Heinz-Peter Breuer,Francesco Petruccione
Publisher : Oxford University Press, USA
Page : 648 pages
File Size : 43,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0198520638

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The Theory of Open Quantum Systems by Heinz-Peter Breuer,Francesco Petruccione Pdf

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.