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Author: Edward Nelson Publisher: Princeton University Press ISBN: 0691079501 Category : Mathematics Languages : en Pages : 147
Book Description
These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.
Author: Edward Nelson Publisher: Princeton University Press ISBN: 0691079501 Category : Mathematics Languages : en Pages : 147
Book Description
These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.
Author: Edward Nelson Publisher: Princeton University Press ISBN: 0691219613 Category : Mathematics Languages : en Pages : 148
Book Description
These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.
Author: Robert M. Mazo Publisher: OUP Oxford ISBN: 0191565083 Category : Science Languages : en Pages : 304
Book Description
Brownian motion - the incessant motion of small particles suspended in a fluid - is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics. A number of new applications of these descriptions to physical and chemical processes, as well as statistical mechanical derivations and the mathematical background are discussed in detail. Graduate students, lecturers, and researchers in statistical physics and physical chemistry will find this an interesting and useful reference work.
Author: Nicola Cufaro Petroni Publisher: Springer Nature ISBN: 3030484084 Category : Science Languages : en Pages : 372
Book Description
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.
Author: Pisin Chen Publisher: World Scientific ISBN: 9789812702333 Category : Science Languages : en Pages : 548
Book Description
This proceedings volume of the 3rd International Workshop on Quantum Aspects of Beam Physics, presents the latest advances in beam dynamics. The frontiers of beam research point to increasingly high energy, greater brightness and lower emittance beams with ever-increasing particle species. These demands have triggered a rapidly growing number of beam phenomena that involve quantum effects. In addition to the more established topics, this volume covers topics on high energy-density particle and photon beams for laboratory astrophysics investigations, as well as the application of beam physics expertise to astrophysics studies. Other exciting new topics are the physics of ultra-cold or condensed beams, such as the ''''crystalline beams'''' and the BoseOCoEinstein condensate ''''atom lasers''''. This book will be a valuable source of reference to readers interested in the interdisciplinary frontiers of ''''quantum beam physics'''' that involve beam physics, particle physics, laser science, astrophysics, condensed matter physics, nuclear and atomic physics. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."
Author: Peter K. Friz Publisher: Springer Nature ISBN: 3030415562 Category : Mathematics Languages : en Pages : 346
Book Description
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Author: Grigorios A. Pavliotis Publisher: Springer ISBN: 1493913239 Category : Mathematics Languages : en Pages : 339
Book Description
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Author: Masao Doi Publisher: Oxford University Press ISBN: 9780198520337 Category : Science Languages : en Pages : 420
Book Description
This book provides a comprehensive account of the modern theory for the dynamical properties of polymer solutions. The theory has undergone dramatic evolution over the last two decades due to the introduction of new methods and concepts that have extended the frontier of theory from dilute solutions in which polymers move independently to concentrated solutions where many polymers converge. Among the properties examined are viscoelasticity, diffusion, dynamic light scattering, and electric birefringence. Nonlinear viscoelasticity is discussed in detail on the basis of molecular dynamical models. The book bridges the gap between classical theory and new developments, creating a consistent picture of polymer solution dynamics over the entire concentration range.
Author: Edward Nelson
Author: Edward Nelson
Author: Enward Neson
Author: Edward Nelson
Author: Edward Nelson
Author: Robert M. Mazo
Author: Nicola Cufaro Petroni
Author: Pisin Chen
Author: Peter K. Friz
Author: Grigorios A. Pavliotis
Author: Masao Doi