The Theory of Open Quantum Systems

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems.

Author: Heinz-Peter Breuer

Publisher: Oxford University Press on Demand

ISBN: 0198520638

Category: Science

Page: 625

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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

In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field.

Author: Ángel Rivas

Publisher: Springer Science & Business Media

ISBN: 3642233546

Category: Science

Page: 97

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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.

Open Quantum Systems II

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.

Author: Stéphane Attal

Publisher: Springer Science & Business Media

ISBN: 9783540309925

Category: Mathematics

Page: 244

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Presents the developments and applications in the field of quantum open systems. This book discusses topics, such as 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.

Open Quantum Systems III

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.

Author: Stéphane Attal

Publisher: Springer Science & Business Media

ISBN: 9783540309932

Category: Mathematics

Page: 314

View: 353

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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.

Open Quantum Systems and Feynman Integrals

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.

Author: P. Exner

Publisher: Springer Science & Business Media

ISBN: 9789400952072

Category: Science

Page: 356

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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.

Open Quantum Systems

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner.

Author: Subhashish Banerjee

Publisher: Springer

ISBN: 9789811331824

Category: Science

Page: 278

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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.

Advances in Open Systems and Fundamental Tests of Quantum Mechanics

This book consists of many contributions addressing the diversified physics community interested in foundations of quantum mechanics and its applications and it reports about recent results in open quantum systems and their connection with ...

Author: Bassano Vacchini

Publisher: Springer Nature

ISBN: 9783030311469

Category: Science

Page: 113

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Quantum mechanics has shown unprecedented success as a physical theory, but it has forced a new view on the description of physical reality. In recent years, important progress has been achieved both in the theory of open quantum systems and in the experimental realization and control of such systems. A great deal of the new results is concerned with the characterization and quantification of quantum memory effects. From this perspective, the 684. WE-Heraeus-Seminar has brought together scientists from different communities, both theoretical and experimental, sharing expertise on open quantum systems, as well as the commitment to the understanding of quantum mechanics. This book consists of many contributions addressing the diversified physics community interested in foundations of quantum mechanics and its applications and it reports about recent results in open quantum systems and their connection with the most advanced experiments testing quantum mechanics.

Open Quantum Systems

This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics.

Author: Dorothea Bahns

Publisher: Springer

ISBN: 9783030130466

Category: Mathematics

Page: 267

View: 642

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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.

An Open Systems Approach to Quantum Optics

This volume contains ten lectures presented in the series ULB Lectures in Nonlinear Optics at the Universite Libre de Bruxelles during the period October 28 to November 4, 1991.

Author: Howard Carmichael

Publisher: Springer Science & Business Media

ISBN: 9783540566342

Category: Computers

Page: 179

View: 201

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This volume contains ten lectures presented in the series ULB Lectures in Nonlinear Optics at the Universite Libre de Bruxelles during the period October 28 to November 4, 1991. A large part of the first six lectures is taken from material prepared for a book of somewhat larger scope which will be published,by Springer under the title Quantum Statistical Methods in Quantum Optics. The principal reason for the early publication of the present volume concerns the material contained in the last four lectures. Here I have put together, in a more or less systematic way, some ideas about the use of stochastic wavefunctions in the theory of open quantum optical systems. These ideas were developed with the help of two of my students, Murray Wolinsky and Liguang Tian, over a period of approximately two years. They are built on a foundation laid down in a paper written with Surendra Singh, Reeta Vyas, and Perry Rice on waiting-time distributions and wavefunction collapse in resonance fluorescence [Phys. Rev. A, 39, 1200 (1989)]. The ULB lecture notes contain my first serious atte~pt to give a complete account of the ideas and their potential applications. I am grateful to Professor Paul Mandel who, through his invitation to give the lectures, stimulated me to organize something useful out of work that may, otherwise, have waited considerably longer to be brought together.

Control of Quantum Systems

Researchers, academics and engineers in quantum engineering, quantum computing, quantum information, quantum communication, quantum physics, and quantum chemistry whose research interests are quantum systems control will find this book ...

Author: Shuang Cong

Publisher: John Wiley & Sons

ISBN: 9781118608159

Category: Technology & Engineering

Page: 448

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Advanced research reference examining the closed and open quantum systems Control of Quantum Systems: Theory and Methods provides an insight into the modern approaches to control of quantum systems evolution, with a focus on both closed and open (dissipative) quantum systems. The topic is timely covering the newest research in the field, and presents and summarizes practical methods and addresses the more theoretical aspects of control, which are of high current interest, but which are not covered at this level in other text books. The quantum control theory and methods written in the book are the results of combination of macro-control theory and microscopic quantum system features. As the development of the nanotechnology progresses, the quantum control theory and methods proposed today are expected to be useful in real quantum systems within five years. The progress of the quantum control theory and methods will promote the progress and development of quantum information, quantum computing, and quantum communication. Equips readers with the potential theories and advanced methods to solve existing problems in quantum optics/information/computing, mesoscopic systems, spin systems, superconducting devices, nano-mechanical devices, precision metrology. Ideal for researchers, academics and engineers in quantum engineering, quantum computing, quantum information, quantum communication, quantum physics, and quantum chemistry, whose research interests are quantum systems control.

Open Quantum Physics and Environmental Heat Conversion into Usable Energy

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 ...

Author: Eliade Stefanescu

Publisher: Bentham Science Publishers

ISBN: 9781608059867

Category: Science

Page: 280

View: 760

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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.

Bohmian Mechanics Open Quantum Systems and Continuous Measurements

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse.

Author: Antonio B. Nassar

Publisher: Springer

ISBN: 3319536516

Category: Science

Page: 250

View: 861

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This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories.

Theory and Application of Open Quantum Systems

Quantum information science is a rapidly growing research area for that it provides new insights to the fundamentals of quantum mechanics and offers a platform for the architecture of novel quantum technologies.

Author: Ching-Kit Chan

Publisher:

ISBN: 1267513616

Category:

Page: 77

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Quantum information science is a rapidly growing research area for that it provides new insights to the fundamentals of quantum mechanics and offers a platform for the architecture of novel quantum technologies. The successfulness and practicality of this important scientific field rely on the controllability of a quantum system subject to a realistic noisy environment. The environment always leads to unintended dynamics of the system, and thus destroys its coherence and limits its applications. It is therefore important to understand these decoherence mechanisms from first principles, in order to minimize, or even remove, its adverse effect on the quantum system. The study of this open quantum system problem is usually based on some effective paradigms, where the environment is assumed to be "large", such that it can affect the quantum system without any back action. However, due to the demand for a high precision in quantum computation, such an approximate framework becomes questionable. We provide a new theoretical approach to treat this type of open quantum system problem, including the correlated dynamics between the system and the environment, by using a diagrammatic technique in the same spirit as the Keldysh non-equilibrium Green's function. In this formalism, both the environment and the photonic control are quantized. The dynamics of the system can be evaluated accurately for a time scale of small decoherence, but arbitrary quantum control, relevant to the need for quantum technologies. This offers a way of precise quantum noise calculations. We find how fundamental quantum correlations between the quantum control and quantum environment can arise, and are missing in the existing Master equation approximations. On the other hand, the study of the environment not only provides a better understanding of the decoherence, it also allows applicable designs of quantum operations between different qubit systems. In particular, we engineer a new protocol to entangle two qubits at a distance by projection measurements of their environments, the resonance fluorescence photons. We find exceptional improvements on the probability of success and the rate of entanglement based on the multiphoton environment approach, in comparison with the existing single photon entanglement scheme.

Open Systems Entanglement and Quantum Optics

The subject of this book is a presentation of some aspects of modern theory of open quantum systems.

Author: Andrzej Jamiolkowski

Publisher: BoD – Books on Demand

ISBN: 9789535111412

Category: Science

Page: 148

View: 330

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The subject of this book is a presentation of some aspects of modern theory of open quantum systems. It introduces several up-to- date topics, such as detecting quantum entanglement, modeling of quantum noise, quantum communication processes, and computational complexity in the analysis of quantum operations. Also discussed are light propagation in optically dressed media, as well as entropy and information measure for quantized electromagnetic fields media. This book is intended for researchers and students interested in the theory of open quantum systems, quantum information theory and quantum systems interacting with electromagnetic fields.

Thermodynamics and Control of Open Quantum Systems

The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum ...

Author: Gershon Kurizki

Publisher: Cambridge University Press

ISBN: 1107175410

Category: Science

Page: 450

View: 926

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The control of open quantum systems and their associated quantum thermodynamic properties is a topic of growing importance in modern quantum physics and quantum chemistry research. This unique and self-contained book presents a unifying perspective of such open quantum systems, first describing the fundamental theory behind these formidably complex systems, before introducing the models and techniques that are employed to control their quantum thermodynamics processes. A detailed discussion of real quantum devices is also covered, including quantum heat engines and quantum refrigerators. The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.