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Author : Sergio A. Albeverio (Mathematician, Switzerland, Germany),Giulio Casati,D. Merlini
Publisher : Unknown
Page : 0 pages
File Size : 53,8 Mb
Release : 1986
Category : Electronic
ISBN : 0387171665
Author : Sergio Albeverio,Giulio Casati,D. Merlini
Publisher : Unknown
Page : 568 pages
File Size : 48,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662135884
Author : Masao Nagasawa
Publisher : Birkhäuser
Page : 609 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883832
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 P. Gudder
Publisher : Courier Corporation
Page : 242 pages
File Size : 44,9 Mb
Release : 2014-05-05
Category : Science
ISBN : 9780486149189
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 : Harish Parthasarathy
Publisher : Taylor & Francis
Page : 275 pages
File Size : 48,8 Mb
Release : 2022-12-23
Category : Science
ISBN : 9781000815542
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Author : Eduard Prugovečki
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 55,8 Mb
Release : 1984-01-31
Category : Gardening
ISBN : 902771617X
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 : Margaret Prugovecki
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400944923
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 : S. Albeverio,P. Combe,M. Sirugue-Collin
Publisher : Springer
Page : 239 pages
File Size : 46,9 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540391388
Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 45,8 Mb
Release : 1991-08-01
Category : Mathematics
ISBN : 9780387971735
Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.
Author : Stéphane Attal,Alain Joye,claude-alain pillet
Publisher : Springer
Page : 244 pages
File Size : 48,6 Mb
Release : 2006-08-29
Category : Mathematics
ISBN : 9783540339663
Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.
Author : Kalyan B. Sinha,Debashish Goswami
Publisher : Cambridge University Press
Page : 301 pages
File Size : 50,9 Mb
Release : 2007-01-25
Category : Mathematics
ISBN : 9781139461696
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
Author : Philipp Strasberg
Publisher : Oxford University Press
Page : 320 pages
File Size : 53,5 Mb
Release : 2021-12-01
Category : Science
ISBN : 9780192648143
The theory of thermodynamics has been one of the bedrocks of 19th-century physics, and thermodynamic problems have inspired Planck's quantum hypothesis. One hundred years later, in an era where we design increasingly sophisticated nanotechnologies, researchers in quantum physics have been 'returning to their roots', attempting to reconcile modern nanoscale devices with the theory of thermodynamics. This textbook explains how it is possible to unify the two opposite pictures of microscopic quantum physics and macroscopic thermodynamics in one consistent framework, proving that the ancient theory of thermodynamics still offers many remarkable insights into present-day problems. This textbook focuses on the microscopic derivation and understanding of key principles and concepts and their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon, and time-reversal symmetry, among other topics. The textbook also explores several practical applications of the theory in more detail, including single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser, and related setups in quantum optics. The aim of this book is to inspire readers to investigate a plethora of modern nanoscale devices from a thermodynamic point of view, allowing them to address their dissipation, efficiency, reliability, and power based on a conceptually clear understanding about the microscopic origin of heat, entropy, and the second law. The book is accessible to graduate students, post-docs, and lecturers, but will also be of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability.
Author : Anonim
Publisher : Unknown
Page : 290 pages
File Size : 54,8 Mb
Release : 2007
Category : Noncommutative differential geometry
ISBN : 0511269412
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
Author : A. O. Bolivar
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 55,8 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096499
At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.
Author : Sergio Chibbaro,Jean-Pierre Minier
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 42,7 Mb
Release : 2013-09-05
Category : Technology & Engineering
ISBN : 9783709116227
Since their first introduction in natural sciences through the work of Einstein on Brownian motion in 1905 and further works, in particular by Langevin, Smoluchowski and others, stochastic processes have been used in several areas of science and technology. For example, they have been applied in chemical studies, or in fluid turbulence and for combustion and reactive flows. The articles in this book provide a general and unified framework in which stochastic processes are presented as modeling tools for various issues in engineering, physics and chemistry, with particular focus on fluid mechanics and notably dispersed two-phase flows. The aim is to develop what can referred to as stochastic modeling for a whole range of applications.