Download or read book Stochastic Methods in Quantum Mechanics written by Stanley P. Gudder and published by Courier Corporation. This book was released on 2014-05-05 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Techniques In Stochastic Mechanics written by John C Baez and published by World Scientific. This book was released on 2018-02-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics written by K.H. Namsrai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Processes in Physics and Chemistry written by N.G. Van Kampen and published by Elsevier. This book was released on 1992-11-20 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.
Download or read book Stochastic Variational Approach to Quantum Mechanical Few Body Problems written by Yasuyuki Suzuki and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Quantum Stochastic Calculus written by K.R. Parthasarathy and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 commutation relations or, equivalently, the uncertainty principle. Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields. Many quantum dynamical semigroups as well as classical Markov semigroups are realised 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. - - - This is an excellent volume which will be a valuable companion both to 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) This monograph gives a systematic and self-contained introduction to the Fock space quantum stochastic calculus in its basic form (...) by making emphasis on the mathematical aspects of quantum formalism and its connections with classical probability and by extensive presentation of carefully selected functional analytic material. This makes the book very convenient for a reader with the probability-theoretic orientation, wishing to make acquaintance with wonders of the noncommutative probability, and, more specifcally, for a mathematics student studying this field. (Zentralblatt MATH) 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)
Download or read book Path Integrals in Physics written by M Chaichian and published by CRC Press. This book was released on 2019-08-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Download or read book Stochastic Quantization written by Mikio Namiki and published by Springer Science & Business Media. This book was released on 2008-10-04 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Stochastics written by Mou-Hsiung Chang and published by Cambridge University Press. This book was released on 2015-02-19 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes for graduate students and researchers. Building a framework that parallels the development of classical probability, it aims to help readers up the steep learning curve of the quantum theory.
Download or read book Quantum Noise written by Crispin Gardiner and published by Springer Science & Business Media. This book was released on 2004-08-27 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quantum amplifier theory, non-Markovian quantum stochastic processes, quantum input--output theory, and positive P-representations. It is the first book in which quantum noise is described by a mathematically complete theory in a form that is also suited to practical applications. Special attention is paid to non-classical effects, such as squeezing and antibunching. Chapters added to the previous edition, on the stochastic Schrödinger equation, and on cascaded quantum systems, and now supplemented, in the third edition by a chapter on recent developments in various pertinent fields such as laser cooling, Bose-Einstein condensation, quantum feedback and quantum information.
Download or read book Statistical Methods in Quantum Optics 1 written by Howard J. Carmichael and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come. The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker-Planck equations.
Download or read book Probability and Stochastic Processes for Physicists written by Nicola Cufaro Petroni and published by Springer Nature. This book was released on 2020-06-25 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probability spaces and measures, random variables, and limit theorems. Here, the focus is mainly on models and ideas rather than the mathematical tools. The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. All these conceptual tools then converge in a dynamical theory of Brownian motion that compares the Einstein–Smoluchowski and Ornstein–Uhlenbeck approaches, highlighting the most important ideas that finally led to a connection between the Schrödinger equation and diffusion processes along the lines of Nelson’s stochastic mechanics. A series of appendices cover particular details and calculations, and offer concise treatments of particular thought-provoking topics.
Download or read book Path Integrals for Stochastic Processes written by Horacio S. Wio and published by World Scientific. This book was released on 2013 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.
Download or read book Handbook of Stochastic Methods written by Crispin W. Gardiner and published by Springer Verlag. This book was released on 1985-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Stochastic Processes in Physics written by Don S. Lemons and published by Johns Hopkins University Press+ORM. This book was released on 2003-04-29 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This “lucid, masterfully written introduction to an often difficult subject . . . belongs on the bookshelf of every student of statistical physics” (Dr. Brian J. Albright, Applied Physics Division, Los Alamos National Laboratory). This book provides an accessible introduction to stochastic processes in physics and describes the basic mathematical tools of the trade: probability, random walks, and Wiener and Ornstein-Uhlenbeck processes. With an emphasis on applications, it includes end-of-chapter problems. Physicist and author Don S. Lemons builds on Paul Langevin’s seminal 1908 paper “On the Theory of Brownian Motion” and its explanations of classical uncertainty in natural phenomena. Following Langevin’s example, Lemons applies Newton’s second law to a “Brownian particle on which the total force included a random component.” This method builds on Newtonian dynamics and provides an accessible explanation to anyone approaching the subject for the first time. This volume contains the complete text of Paul Langevin’s “On the Theory of Brownian Motion,” translated by Anthony Gythiel.
Download or read book Stochastic Processes written by Wolfgang Paul and published by Springer Science & Business Media. This book was released on 2013-07-11 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.
Download or read book Statistical Mechanics Kinetic theory and Stochastic Processes written by C.V. Heer and published by Elsevier. This book was released on 2012-12-02 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Mechanics, Kinetic Theory, and Stochastic Processes presents the statistical aspects of physics as a "living and dynamic" subject. In order to provide an elementary introduction to kinetic theory, physical systems in which particle-particle interaction can be neglected are considered. Transport phenomena in the free-molecular flow region for gases and the transport of thermal radiation are discussed. Discrete random processes such as random walk, binomial and Poisson distributions, and throwing of dice are studied by means of the characteristic function. Comprised of 11 chapters, this book begins with an introduction to the mass point gas as well as some elementary properties of space and velocity distributions. The discussion then turns to radiation and its interaction with an atom; probability, statistics, and conditional probability; intermolecular interactions; transport phenomena; and statistical thermodynamics. Molecular systems at low densities are also considered, together with non-ideal and real gases; liquids and solids; and stochastic processes, noise, and fluctuations. In particular, the response of atoms and molecules to perturbations and scattering by crystals, liquids, and high-pressure gases are examined. This monograph will be useful for undergraduate students, practitioners, and researchers in physics.
