Quantum Dynamical Systems

Author : Robert Alicki,Institute of Theoretical Physics and Astrophysics Robert Alicki,M. Fannes
Publisher : Oxford University Press on Demand
Page : 278 pages
File Size : 40,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0198504004

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Quantum Dynamical Systems by Robert Alicki,Institute of Theoretical Physics and Astrophysics Robert Alicki,M. Fannes Pdf

The present book provides a unified and general framework for studying quantum and classical dynamical systems, both finite and infinite, conservative and dissipative. Special attention is paid to the use of statistical and geometrical techniques, such as multitime correlation functions,quantum dynamical entropy, and non-commutative Lyapunov exponents, for systems with a complex evolution. The material is presented in a concise but self-contained and mathematically friendly way. The main ideas are introduced and illustrated by numerous examples which are directly connected to therelevant physics. Suggestions for further reading are included at the end of each chapter. The book addresses graduate students both in physics and mathematics with interests in mathematical aspects of quantum physics and applications of ergodic theory, operator algebras and statistics to physics,but without any prior knowledge of these subjects.

Author : Fabio Benatti
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 42,6 Mb
Release : 2009-04-17
Category : Computers
ISBN : 9781402093067

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Dynamics, Information and Complexity in Quantum Systems by Fabio Benatti Pdf

This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.

Author : Hendra I Nurdin,Naoki Yamamoto
Publisher : Springer
Page : 262 pages
File Size : 47,5 Mb
Release : 2017-05-11
Category : Technology & Engineering
ISBN : 9783319552019

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Linear Dynamical Quantum Systems by Hendra I Nurdin,Naoki Yamamoto Pdf

This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics will find this book to be a valuable treatment of the control of an important class of quantum systems. The material presented here will also interest physicists working in optics, quantum optics, quantum information theory and other quantum-physical disciplines.

Author : Sergio Albeverio,Rodolfo Figari,Enza Orlandi,Alessandro Teta
Publisher : World Scientific
Page : 374 pages
File Size : 55,7 Mb
Release : 1995-02-23
Category : Electronic
ISBN : 9789814550628

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Advances In Dynamical Systems And Quantum Physics - Proceedings Of The Conference by Sergio Albeverio,Rodolfo Figari,Enza Orlandi,Alessandro Teta Pdf

This volume contains contributions from the meeting held in honour of G.F. Dell'Antonio for his sixtieth birthday. The topics covered include the theory of classical and quantum dynamical systems and related mathematical disciplines such as functional and stochastic analysis, operator algebras etc. The contributions by leading specialists survey recent developments in Hamiltonian dynamics, non-commutative integration, supersymmetric theories, spin glass theory and other subjects in mathematical physics.

Author : Robert Alicki,K. Lendi
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 49,7 Mb
Release : 2007-04-23
Category : Science
ISBN : 9783540708605

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Quantum Dynamical Semigroups and Applications by Robert Alicki,K. Lendi Pdf

Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention. This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

Author : Fabio Bagarello
Publisher : John Wiley & Sons
Page : 186 pages
File Size : 42,6 Mb
Release : 2012-10-11
Category : Science
ISBN : 9781118400609

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Quantum Dynamics for Classical Systems by Fabio Bagarello Pdf

Introduces number operators with a focus on the relationship between quantum mechanics and social science Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models Illustrations of the use of creation and annihilation operators for classical problems Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field Quantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models.

Author : Fabio Benatti
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642849992

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Deterministic Chaos in Infinite Quantum Systems by Fabio Benatti Pdf

The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.

Author : Vladimir M. Akulin
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 42,9 Mb
Release : 2005-12-21
Category : Science
ISBN : 9783540292715

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Coherent Dynamics of Complex Quantum Systems by Vladimir M. Akulin Pdf

Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.

Author : Sandro Wimberger
Publisher : Springer Nature
Page : 270 pages
File Size : 55,9 Mb
Release : 2023-01-01
Category : Science
ISBN : 9783031012495

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : A. Blaquiere,S. Diner,G. Lochak
Publisher : Springer
Page : 356 pages
File Size : 40,8 Mb
Release : 2014-05-04
Category : Science
ISBN : 9783709129715

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Information Complexity and Control in Quantum Physics by A. Blaquiere,S. Diner,G. Lochak Pdf

Author : Larry Meredith Bates,David Lawrence Rod
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 51,7 Mb
Release : 1996
Category : Science
ISBN : 9780821802540

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Conservative Systems and Quantum Chaos by Larry Meredith Bates,David Lawrence Rod Pdf

This volume presents new research in classical Hamiltonian and quantum systems from the Workshop on Conservative Systems and Quantum Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in October 1992 (Waterloo, Canada). The workshop was organized so that there were presentations that formed a bridge between classical and quantum mechanical systems. Four of these papers appear in this collection, with the remaining six papers concentrating on classical Hamiltonian dynamics.

Author : J.M. Souriau
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202813

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Structure of Dynamical Systems by J.M. Souriau Pdf

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 47,9 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789400914834

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Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models by Andrei Y. Khrennikov Pdf

N atur non facit saltus? This book is devoted to the fundamental problem which arises contin uously in the process of the human investigation of reality: the role of a mathematical apparatus in a description of reality. We pay our main attention to the role of number systems which are used, or may be used, in this process. We shall show that the picture of reality based on the standard (since the works of Galileo and Newton) methods of real analysis is not the unique possible way of presenting reality in a human brain. There exist other pictures of reality where other num ber fields are used as basic elements of a mathematical description. In this book we try to build a p-adic picture of reality based on the fields of p-adic numbers Qp and corresponding analysis (a particular case of so called non-Archimedean analysis). However, this book must not be considered as only a book on p-adic analysis and its applications. We study a much more extended range of problems. Our philosophical and physical ideas can be realized in other mathematical frameworks which are not obliged to be based on p-adic analysis. We shall show that many problems of the description of reality with the aid of real numbers are induced by unlimited applications of the so called Archimedean axiom.

Author : Sandro Wimberger
Publisher : Springer
Page : 215 pages
File Size : 53,8 Mb
Release : 2014-05-13
Category : Science
ISBN : 9783319063430

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : Gennadiĭ Alekseevich Leonov,V. Reitmann,W. Timmermann
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 1990
Category : Electronic
ISBN : 3055008588

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Nonlinear Dynamics and Quantum Dynamical Systems by Gennadiĭ Alekseevich Leonov,V. Reitmann,W. Timmermann Pdf