Open Quantum Systems And Feynman Integrals
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Author | : P. Exner |
Publisher | : Springer Science & Business Media |
Total Pages | : 374 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9400952074 |
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Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory. The present volume is devoted to this problem: we shall be concerned with open quantum systems, i.e. those that cannot be regarded as isolated from the rest of the physical universe. It is a natural framework in which non-stationary processes can be investigated. There are two main approaches to the treatment of open systems in quantum theory. In both the system under consideration is viewed as part of a larger system, assumed to be isolated in a reasonable approximation. They are differentiated mainly by the way in which the state Hilbert space of the open system is related to that of the isolated system - either by orthogonal sum or by tensor product. Though often applicable simultaneously to the same physical situation, these approaches are complementary in a sense and are adapted to different purposes. Here we shall be concerned with the first approach, which is suitable primarily for a description of decay processes, absorption, etc. The second approach is used mostly for the treatment of various relaxation phenomena. It is comparably better examined at present; in particular, the reader may consult a monograph by E. B. Davies.
Author | : Pavel Exner |
Publisher | : |
Total Pages | : 380 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9789400952089 |
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Author | : Z. Haba |
Publisher | : Springer Science & Business Media |
Total Pages | : 378 |
Release | : 2013-03-11 |
Genre | : Science |
ISBN | : 9401147167 |
Download Feynman Integral and Random Dynamics in Quantum Physics Book in PDF, Epub and Kindle
The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics.
Author | : Sergio Albeverio |
Publisher | : Springer |
Total Pages | : 184 |
Release | : 2008-05-06 |
Genre | : Mathematics |
ISBN | : 3540769560 |
Download Mathematical Theory of Feynman Path Integrals Book in PDF, Epub and Kindle
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Author | : Ángel Rivas |
Publisher | : Springer Science & Business Media |
Total Pages | : 103 |
Release | : 2011-10-01 |
Genre | : Science |
ISBN | : 3642233546 |
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In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.
Author | : Sonia Mazzucchi |
Publisher | : World Scientific |
Total Pages | : 225 |
Release | : 2009-05-22 |
Genre | : Science |
ISBN | : 9814469270 |
Download Mathematical Feynman Path Integrals And Their Applications Book in PDF, Epub and Kindle
Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman's ideas.This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author.Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.
Author | : Sonia Mazzucchi |
Publisher | : World Scientific |
Total Pages | : 360 |
Release | : 2021-11-16 |
Genre | : Science |
ISBN | : 9811214808 |
Download Mathematical Feynman Path Integrals And Their Applications (Second Edition) Book in PDF, Epub and Kindle
Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.
Author | : Richard P. Feynman |
Publisher | : Courier Corporation |
Total Pages | : 386 |
Release | : 2010-07-21 |
Genre | : Science |
ISBN | : 0486477223 |
Download Quantum Mechanics and Path Integrals Book in PDF, Epub and Kindle
Looks at quantum mechanics, covering such topics as perturbation method, statistical mechanics, path integrals, and quantum electrodynamics.
Author | : Richard Phillips Feynman |
Publisher | : McGraw-Hill Companies |
Total Pages | : 392 |
Release | : 1965 |
Genre | : Science |
ISBN | : |
Download Quantum Mechanics and Path Integrals Book in PDF, Epub and Kindle
The fundamental concepts of quantum mechanics -- The quantum-mechanical law of motion -- Developing the concepts with special examples -- The Schrödinger description of quantum mechanics -- Measurements and operators -- The perturbation method in quantum mechanics -- Transition elements -- Harmonic oscillators -- Quantum electrodynamics -- Statistical mechanics -- The variational method -- Other problems in probability.
Author | : Lukong Cornelius Fai |
Publisher | : CRC Press |
Total Pages | : 394 |
Release | : 2021-04-16 |
Genre | : Science |
ISBN | : 1000349063 |
Download Feynman Path Integrals in Quantum Mechanics and Statistical Physics Book in PDF, Epub and Kindle
This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.