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

Author : Konstantin A Makarov,Eduard R Tsekanovskii
Publisher : World Scientific
Page : 300 pages
File Size : 49,8 Mb
Release : 2021-12-24
Category : Science
ISBN : 9789811241246

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Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements by Konstantin A Makarov,Eduard R Tsekanovskii Pdf

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.

Author : Stéphane Attal
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 46,5 Mb
Release : 2006-06-07
Category : Mathematics
ISBN : 9783540309932

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Open Quantum Systems III by Stéphane Attal Pdf

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.

Author : Heinz-Peter Breuer,Francesco Petruccione
Publisher : Oxford University Press, USA
Page : 648 pages
File Size : 51,8 Mb
Release : 2002
Category : Mathematics
ISBN : 0198520638

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The Theory of Open Quantum Systems by Heinz-Peter Breuer,Francesco Petruccione Pdf

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.

Author : Stéphane Attal,Alain Joye,claude-alain pillet
Publisher : Springer
Page : 329 pages
File Size : 50,9 Mb
Release : 2006-06-07
Category : Mathematics
ISBN : 3540309918

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Open Quantum Systems I by Stéphane Attal,Alain Joye,claude-alain pillet Pdf

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 : Stéphane Attal,Alain Joye,Claude-Alain Pillet
Publisher : Springer
Page : 254 pages
File Size : 44,9 Mb
Release : 2006-08-29
Category : Mathematics
ISBN : 9783540339663

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Open Quantum Systems II by Stéphane Attal,Alain Joye,Claude-Alain Pillet Pdf

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 : Stéphane Attal,Alain Joye,claude-alain pillet
Publisher : Springer
Page : 329 pages
File Size : 47,7 Mb
Release : 2006-08-18
Category : Mathematics
ISBN : 9783540339229

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Open Quantum Systems I by Stéphane Attal,Alain Joye,claude-alain pillet Pdf

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 : Dorothea Bahns,Anke Pohl,Ingo Witt
Publisher : Springer
Page : 267 pages
File Size : 42,8 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9783030130466

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Open Quantum Systems by Dorothea Bahns,Anke Pohl,Ingo Witt Pdf

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.

Author : Edward Brian Davies
Publisher : Unknown
Page : 192 pages
File Size : 42,7 Mb
Release : 1976
Category : Mathematics
ISBN : UCAL:B4523392

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Quantum Theory of Open Systems by Edward Brian Davies Pdf

Author : Ángel Rivas,Susana F. Huelga
Publisher : Springer Science & Business Media
Page : 103 pages
File Size : 51,8 Mb
Release : 2011-10-01
Category : Science
ISBN : 9783642233548

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Open Quantum Systems by Ángel Rivas,Susana F. Huelga Pdf

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 : Nieuwenhuizen Theo M,Pombo Claudia,Furtado Claudio
Publisher : World Scientific
Page : 612 pages
File Size : 52,9 Mb
Release : 2014-10-03
Category : Science
ISBN : 9789814616744

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Quantum Foundations And Open Quantum Systems: Lecture Notes Of The Advanced School by Nieuwenhuizen Theo M,Pombo Claudia,Furtado Claudio Pdf

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.

Author : Ulrich Weiss
Publisher : World Scientific
Page : 607 pages
File Size : 43,5 Mb
Release : 2021-09-21
Category : Science
ISBN : 9789811241512

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Quantum Dissipative Systems (Fifth Edition) by Ulrich Weiss Pdf

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.

Author : Ulrich Weiss
Publisher : World Scientific
Page : 527 pages
File Size : 40,7 Mb
Release : 2008
Category : Science
ISBN : 9789812791627

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Quantum Dissipative Systems by Ulrich Weiss Pdf

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.

Author : Eliade Stefanescu
Publisher : Bentham Science Publishers
Page : 279 pages
File Size : 48,8 Mb
Release : 2014-12-18
Category : Science
ISBN : 9781608059867

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Open Quantum Physics and Environmental Heat Conversion into Usable Energy by Eliade Stefanescu Pdf

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.

Author : K. Kong Wan
Publisher : World Scientific
Page : 712 pages
File Size : 47,7 Mb
Release : 2006
Category : Science
ISBN : 9781860946257

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From Micro to Macro Quantum Systems by K. Kong Wan Pdf

Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations.This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schr”dinger's cat states in superconducting systems, and a path space formulation of quantum mechanics.This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators.

Author : Marco Tomamichel
Publisher : Springer
Page : 138 pages
File Size : 53,5 Mb
Release : 2015-10-14
Category : Science
ISBN : 9783319218915

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Quantum Information Processing with Finite Resources by Marco Tomamichel Pdf

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.