Mathematics Of Open Quantum Systems The Dissipative And Non Unitary Representations And Quantum Measurements

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Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements

Author : Konstantin A Makarov
Publisher : World Scientific
ISBN 13 : 9811241244
Total Pages : 300 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements by : Konstantin A Makarov

Download or read book Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements written by Konstantin A Makarov and published by World Scientific. This book was released on 2021-12-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory.In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs.The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated 'double-slit experiment' where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring.

Open Quantum Systems III

Author : Stéphane Attal
Publisher : Springer Science & Business Media
ISBN 13 : 3540309934
Total Pages : 326 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Open Quantum Systems III by : Stéphane Attal

Download or read book Open Quantum Systems III written by Stéphane Attal and published by Springer Science & Business Media. This book was released on 2006-06-07 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.

The Theory of Open Quantum Systems

Author : Heinz-Peter Breuer
Publisher : Oxford University Press, USA
ISBN 13 : 9780198520634
Total Pages : 648 pages
Book Rating : 4.5/5 (26 download)

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Book Synopsis The Theory of Open Quantum Systems by : Heinz-Peter Breuer

Download or read book The Theory of Open Quantum Systems written by Heinz-Peter Breuer and published by Oxford University Press, USA. This book was released on 2002 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

Open Quantum Systems I

Author : Stéphane Attal
Publisher : Springer
ISBN 13 : 9783540309918
Total Pages : 329 pages
Book Rating : 4.3/5 (99 download)

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Book Synopsis Open Quantum Systems I by : Stéphane Attal

Download or read book Open Quantum Systems I written by Stéphane Attal and published by Springer. This book was released on 2006-06-07 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Open Quantum Systems I

Author : Stéphane Attal
Publisher : Springer
ISBN 13 : 3540339221
Total Pages : 329 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Open Quantum Systems I by : Stéphane Attal

Download or read book Open Quantum Systems I written by Stéphane Attal and published by Springer. This book was released on 2006-08-18 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Open Quantum Systems II

Author : Stéphane Attal
Publisher : Springer
ISBN 13 : 3540339663
Total Pages : 254 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Open Quantum Systems II by : Stéphane Attal

Download or read book Open Quantum Systems II written by Stéphane Attal and published by Springer. This book was released on 2006-08-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Open Quantum Systems

Author : Dorothea Bahns
Publisher : Springer
ISBN 13 : 3030130460
Total Pages : 267 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Open Quantum Systems by : Dorothea Bahns

Download or read book Open Quantum Systems written by Dorothea Bahns and published by Springer. This book was released on 2019-06-28 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Quantum Theory of Open Systems

Author : Edward Brian Davies
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (45 download)

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Book Synopsis Quantum Theory of Open Systems by : Edward Brian Davies

Download or read book Quantum Theory of Open Systems written by Edward Brian Davies and published by . This book was released on 1976 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Open Quantum Systems

Author : Ángel Rivas
Publisher : Springer Science & Business Media
ISBN 13 : 3642233546
Total Pages : 103 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Open Quantum Systems by : Ángel Rivas

Download or read book Open Quantum Systems written by Ángel Rivas and published by Springer Science & Business Media. This book was released on 2011-10-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Foundations And Open Quantum Systems: Lecture Notes Of The Advanced School

Author : Nieuwenhuizen Theo M
Publisher : World Scientific
ISBN 13 : 9814616745
Total Pages : 612 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Quantum Foundations And Open Quantum Systems: Lecture Notes Of The Advanced School by : Nieuwenhuizen Theo M

Download or read book Quantum Foundations And Open Quantum Systems: Lecture Notes Of The Advanced School written by Nieuwenhuizen Theo M and published by World Scientific. This book was released on 2014-10-03 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advanced School on Quantum Foundations and Open Quantum Systems was an exceptional combination of lectures. These comprise lectures in standard physics and investigations on the foundations of quantum physics.On the one hand it included lectures on quantum information, quantum open systems, quantum transport and quantum solid state. On the other hand it included lectures on quantum measurement, models for elementary particles, sub-quantum structures and aspects on the philosophy and principles of quantum physics.The special program of this school offered a broad outlook on the current and near future fundamental research in theoretical physics.The lectures are at the level of PhD students.

Quantum Dissipative Systems (Fifth Edition)

Author : Ulrich Weiss
Publisher : World Scientific
ISBN 13 : 9811241511
Total Pages : 607 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Quantum Dissipative Systems (Fifth Edition) by : Ulrich Weiss

Download or read book Quantum Dissipative Systems (Fifth Edition) written by Ulrich Weiss and published by World Scientific. This book was released on 2021-09-21 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook provides the fundamental concepts and methods of dissipative quantum mechanics and related issues in condensed matter physics starting from first principles. It deals with the phenomena and theory of decoherence, relaxation and dissipation in quantum mechanics that arise from the random exchange of energy with the environment. Major theoretical advances in combination with stunning experimental achievements and the arising perspective for quantum computing have brightened the field and brought it to the attention of the general community in natural sciences. Expertise in dissipative quantum mechanics is by now beneficial in a broad sphere.This book — originally published in 1992 and republished as enlarged and updated second, third and fourth edition in 1999, 2008, and 2012 — dives even deeper into the fundamental concepts, methods and applications of quantum dissipation. The fifth edition provides a self-contained and updated account of the quantum mechanics and quantum statistics of open systems. The subject matter of the book has been thoroughly revised to better comply with the needs of newcomers and the demands of the advanced readership. Most of the chapters are rewritten to enhance clarity and topicality. Four new chapters covering recent developments in the field have been added. There are about 600 references. This book is intended for use by advanced undergraduate and graduate students in physics, and for researchers active in the field. They will find the monograph as a rich and stimulating source.

Noncommutative Mathematics for Quantum Systems

Author : Uwe Franz
Publisher : Cambridge University Press
ISBN 13 : 1316674045
Total Pages : 200 pages
Book Rating : 4.3/5 (166 download)

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Book Synopsis Noncommutative Mathematics for Quantum Systems by : Uwe Franz

Download or read book Noncommutative Mathematics for Quantum Systems written by Uwe Franz and published by Cambridge University Press. This book was released on 2016-01-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.

Open Quantum Systems

Author : Subhashish Banerjee
Publisher : Texts and Readings in Physical
ISBN 13 : 9789811348150
Total Pages : 298 pages
Book Rating : 4.3/5 (481 download)

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Book Synopsis Open Quantum Systems by : Subhashish Banerjee

Download or read book Open Quantum Systems written by Subhashish Banerjee and published by Texts and Readings in Physical. This book was released on 2019-11-26 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

Quantum Dissipative Systems

Author : Ulrich Weiss
Publisher : World Scientific
ISBN 13 : 9812791620
Total Pages : 527 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Quantum Dissipative Systems by : Ulrich Weiss

Download or read book Quantum Dissipative Systems written by Ulrich Weiss and published by World Scientific. This book was released on 2008 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major advances in the quantum theory of macroscopic systems, in combination with experimental achievements, have brightened the field and brought it to the attention of the general community in natural sciences. This edition delves deeper into the fundamental concepts, methods, and applications of quantum dissipative systems.

Open Quantum Physics and Environmental Heat Conversion into Usable Energy

Author : Eliade Stefanescu
Publisher : Bentham Science Publishers
ISBN 13 : 1608059863
Total Pages : 279 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Open Quantum Physics and Environmental Heat Conversion into Usable Energy by : Eliade Stefanescu

Download or read book Open Quantum Physics and Environmental Heat Conversion into Usable Energy written by Eliade Stefanescu and published by Bentham Science Publishers. This book was released on 2014-12-18 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Quantum system can be viewed as a larger closed system comprising of two components: an open quantum system and its surrounding environment. These two components interact with each other, and in the realm of theoretical physics, this interaction cannot be neglected. This eBook explains mathematical and statistical concepts essential for describing a realistic quantum system by presenting recent contributions in this field. The book commences by explaining of the basics of quantum mechanics, statistical physics, and physics of open quantum systems. Detailed methods of deriving theoretical equations with explicit analytical coefficients with respect to open quantum systems are also explained. The book concludes with the study of a quantum heat converter in the framework of an all-microscopic theory involving fermions, photons, and phonons. Readers of this book will gain a better understanding on the following topics: • Quantum mechanics including the Boson and Fermion states, Fermi-Dirac and Bose-Einstein statistics, spin-statistics relation, many-body systems of Bosons and Fermions, the Fermi-Dirac integrals of the Fermion state densities, and transport phenomena in semiconductors • Dissipative dynamics and quantum systems such as friction, diffusion, friction-diffusion relation, mobility, occupation probability dynamics, damping, spectral width, correlation and autocorrelation, memory, stability, bifurcation, self-organization, and chaos • Lindblad’s theory of open quantum systems through the work of Alicki and Lendi • Quantum tunneling as an interaction with a system. • Optical bistability, including the fundamental contributions of Carmichael, McCall, and Bonifacio. • Master equations based on the microscopic theory of Ford, Lewis, and O’Connell. • Field propagation in a semiconductor structure • Coherent light propagation in the framework of a microscopic model including the refractive index and the Raman frequency shift. • Heat conversion in the framework of an all-microscopic model of open queantum systems • Entropy dynamics in a matter field system.

Quantum Trajectories and Measurements in Continuous Time

Author : Alberto Barchielli
Publisher : Springer
ISBN 13 : 9783642012990
Total Pages : 325 pages
Book Rating : 4.0/5 (129 download)

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Book Synopsis Quantum Trajectories and Measurements in Continuous Time by : Alberto Barchielli

Download or read book Quantum Trajectories and Measurements in Continuous Time written by Alberto Barchielli and published by Springer. This book was released on 2009-08-31 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum trajectory theory is largely employed in theoretical quantum optics and quantum open system theory and is closely related to the conceptual formalism of quantum mechanics (quantum measurement theory). However, even research articles show that not all the features of the theory are well known or completely exploited. We wrote this monograph mainly for researchers in theoretical quantum optics and related ?elds with the aim of giving a self-contained and solid p- sentation of a part of quantum trajectory theory (the diffusive case) together with some signi?cant applications (mainly with purposes of illustration of the theory, but which in part have been recently developed). Another aim of the monograph is to introduce to this subject post-graduate or PhD students. To help them, in the most mathematical and conceptual chapters, summaries are given to ?x ideas. Moreover, as stochastic calculus is usually not in the background of the studies in physics, we added Appendix A to introduce these concepts. The book is written also for ma- ematicians with interests in quantum theories. Quantum trajectory theory is a piece of modern theoretical physics which needs an interplay of various mathematical subjects, such as functional analysis and probability theory (stochastic calculus), and offers to mathematicians a beautiful ?eld for applications, giving suggestions for new mathematical developments.

Quantum Information Processing with Finite Resources

Author : Marco Tomamichel
Publisher : Springer
ISBN 13 : 3319218913
Total Pages : 138 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Quantum Information Processing with Finite Resources by : Marco Tomamichel

Download or read book Quantum Information Processing with Finite Resources written by Marco Tomamichel and published by Springer. This book was released on 2015-10-14 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.