Stochastics And Quantum Mechanics

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Stochastic Quantum Mechanics and Quantum Spacetime

Eduard Prugovečki
Stochastic Quantum Mechanics and Quantum Spacetime Book PDF

Author : Eduard Prugovečki
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 42,6 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.

Stochastic Processes in Quantum Physics

Masao Nagasawa
Stochastic Processes in Quantum Physics Book PDF

Author : Masao Nagasawa
Publisher : Birkhäuser
Page : 609 pages
File Size : 46,5 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

Quantum Techniques In Stochastic Mechanics

Baez John C,Biamonte Jacob D
Quantum Techniques In Stochastic Mechanics Book PDF

Author : Baez John C,Biamonte Jacob D
Publisher : World Scientific
Page : 276 pages
File Size : 42,6 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

Stochastic Methods in Quantum Mechanics

Stanley P. Gudder
Stochastic Methods in Quantum Mechanics Book PDF

Author : Stanley P. Gudder
Publisher : Courier Corporation
Page : 242 pages
File Size : 53,9 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.

Stochastics And Quantum Mechanics

Ian M Davies,Aubrey Truman
Stochastics And Quantum Mechanics Book PDF

Author : Ian M Davies,Aubrey Truman
Publisher : World Scientific
Page : 326 pages
File Size : 40,7 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.

Stochastic Quantum Mechanics and Quantum Spacetime

Margaret Prugovecki
Stochastic Quantum Mechanics and Quantum Spacetime Book PDF

Author : Margaret Prugovecki
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 41,5 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.

Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics

K.H. Namsrai
Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics Book PDF

Author : K.H. Namsrai
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 51,9 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.

Quantum Theory and Its Stochastic Limit

Luigi Accardi,Yun Gang Lu,Igor Volovich
Quantum Theory and Its Stochastic Limit Book PDF

Author : Luigi Accardi,Yun Gang Lu,Igor Volovich
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 43,9 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.

Markov Processes and Quantum Theory

Masao Nagasawa
Markov Processes and Quantum Theory Book PDF

Author : Masao Nagasawa
Publisher : Springer Nature
Page : 339 pages
File Size : 54,7 Mb
Release : 2021-06-23
Category : Computers
ISBN : 9783030626884

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Markov Processes and Quantum Theory by Masao Nagasawa Pdf

This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schrödinger equation is a complex-valued evolution equation and the Schrödinger function is a complex-valued evolution function, important applications are given. Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.

Stochastic Mechanics and Stochastic Processes

Aubrey Truman,Ian M. Davies
Stochastic Mechanics and Stochastic Processes Book PDF

Author : Aubrey Truman,Ian M. Davies
Publisher : Springer
Page : 227 pages
File Size : 46,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540458876

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Stochastic Mechanics and Stochastic Processes by Aubrey Truman,Ian M. Davies Pdf

The main theme of the meeting was to illustrate the use of stochastic processes in the study of topological problems in quantum physics and statistical mechanics. Much discussion of current problems was generated and there was a considerable amount of interaction between mathematicians and physicists. The papers presented in the proceedings are essentially of a research nature but some (Lewis, Hudson) are introductions or surveys.

An Introduction to Quantum Stochastic Calculus

K.R. Parthasarathy
An Introduction to Quantum Stochastic Calculus Book PDF

Author : K.R. Parthasarathy
Publisher : Birkhäuser
Page : 299 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886413

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An Introduction to Quantum Stochastic Calculus by K.R. Parthasarathy Pdf

"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.

Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems

Yasuyuki Suzuki,Kalman Varga
Stochastic Variational Approach to Quantum Mechanical Few Body Problems Book PDF

Author : Yasuyuki Suzuki,Kalman Varga
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 51,7 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540495413

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Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems by Yasuyuki Suzuki,Kalman Varga Pdf

The quantum-mechanical few-body problem is of fundamental importance for all branches of microphysics and it has substantially broadened with the advent of modern computers. This book gives a simple, unified recipe to obtain precise solutions to virtually any few-body bound-state problem and presents its application to various problems in atomic, molecular, nuclear, subnuclear and solid state physics. The main ingredients of the methodology are a wave-function expansion in terms of correlated Gaussians and an optimization of the variational trial function by stochastic sampling. The book is written for physicists and, especially, for graduate students interested in quantum few-body physics.

Quantum Mechanics

Ramabhadra Vasudevan,R. Ramanathan
Quantum Mechanics Book PDF

Author : Ramabhadra Vasudevan,R. Ramanathan
Publisher : Alpha Science International, Limited
Page : 316 pages
File Size : 44,5 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.

Stochastic Methods in Quantum Mechanics

Stanley Gudder
Stochastic Methods in Quantum Mechanics Book PDF

Author : Stanley Gudder
Publisher : Unknown
Page : 219 pages
File Size : 54,7 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.

The Quantum Dice

Luis de la Peña,A.M. Cetto
The Quantum Dice Book PDF

Author : Luis de la Peña,A.M. Cetto
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 53,6 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401587235

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The Quantum Dice by Luis de la Peña,A.M. Cetto Pdf

In spite of the impressive predictive power and strong mathematical structure of quantum mechanics, the theory has always suffered from important conceptual problems. Some of these have never been solved. Motivated by this state of affairs, a number of physicists have worked together for over thirty years to develop stochastic electrodynamics, a physical theory aimed at finding a conceptually satisfactory, realistic explanation of quantum phenomena. This is the first book to present a comprehensive review of stochastic electrodynamics, from its origins to present-day developments. After a general introduction for the non-specialist, a critical discussion is presented of the main results of the theory as well as of the major problems encountered. A chapter on stochastic optics and some interesting consequences for local realism and the Bell inequalities is included. In the final chapters the authors propose and develop a new version of the theory that brings it in closer correspondence with quantum mechanics and sheds some light on the wave aspects of matter and the linkage with quantum electrodynamics. Audience: The volume will be of interest to scholars and postgraduate students of theoretical and mathematical physics, foundations and philosophy of physics, and teachers of theoretical physics and quantum mechanics, electromagnetic theory, and statistical physics (stochastic processes).