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Author: K. Kong Wan Publisher: World Scientific ISBN: 1860946259 Category : Science Languages : en Pages : 712
Book Description
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, Schrdinger'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: K. Kong Wan Publisher: World Scientific ISBN: 1860946259 Category : Science Languages : en Pages : 712
Book Description
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, Schrdinger'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: Vlatko Vedral Publisher: World Scientific ISBN: 9813229535 Category : Science Languages : en Pages : 193
Book Description
This is a popular science book exploring the limits of scientific explanation. In particular, it debates if all sciences will ultimately be reducible to physics. The journey starts with physics itself, where there is a gap between the micro (quantum) and the macro (classical) and moves into chemistry, biology and the social sciences. Written by a practising scientist, this volume offers a personal perspective on various topics and incorporates the latest research.
Author: Mark Fannes Publisher: Springer Science & Business Media ISBN: 1461524601 Category : Science Languages : en Pages : 467
Book Description
This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.
Author: Izumi Ojima Publisher: World Scientific Publishing Company ISBN: 9789813238367 Category : Languages : en Pages : 300
Book Description
According to the fundamental concept 'adjunctions' in category theory, the Micro and Macro in nature can be connected in a coherent way, which constitutes quite an effective theoretical and mathematical machinery that has not been commonly recognized. On the basis of this concept, many important problems in physics and mathematics can be viewed from quite different and fresh angles, which facilitate deep understanding and the satisfactory solution of those problems.
Author: Bernardo A. Huberman Publisher: World Scientific ISBN: 9789810209827 Category : Computers Languages : en Pages : 182
Book Description
The laws and methodology of physics are starting to provide powerful insights into the nature and dynamics of computation. This book contains a number of articles that illustrate how fields ranging from quantum mechanics to statistical physics and nonlinear dynamics can help elucidate the nature of computation.
Author: Stephen J. Gustafson Publisher: Springer Science & Business Media ISBN: 3642218660 Category : Mathematics Languages : en Pages : 380
Book Description
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.
Author: Zoran Majkic Publisher: ISBN: 9781536172003 Category : Languages : en Pages : 455
Book Description
Quantum mechanics, based on the Schrödinger equation (and its relativistic Dirac's extension) is a statistical theory, here denominated as Statistical Quantum Mechanics (SQM), to differentiate it from the new part of the quantum theory, provided in PART I and II, denominated Individual-particles Quantum Mechanics (IQM). Both of them are necessary components of the quantum theory, as are the Classical Mechanics for Individual objects (ICM), based on the Newton equations, Hamiltonian-Jacobi equations or the Euler-Lagrange equation of motion of individual objects, and the Statistical Classical Mechanics (SCM) based on the Liouville equations. The SQM tells us the various possible outcomes of experiments and the corresponding probabilities if we would do a large number of identical experiments on individual quantum systems. The SQM systems are not all identical but this is the same type of fluctuation that occurs in classical statistical descriptions in SCM. At first sight the situation may not appear very different therefore from the description provided by classical statistical mechanics. In that case however, we have an underlying description (ICM) that provides a complete (i.e. non-statistical) description of the world, which in general is far too complex, however, to be of use.The last PART III of this trilogy is dedicated to the completion of the whole theoretical mechanics, both classical and quantum inside a 9-D time-space manifold of the Universe. Only in this final third volume, this IQM theory, dedicated in the first two volumes only to the elementary particles, is extended also to the non-elementary particles (like hadrons, nucleus, atoms, molecules, and all every-day objects in our common life, up to the biggest non-elementary particles, like the planets, stars, etc.) in our unique Universe.So, each object in our Universe, from the smallest (elementary) to the biggest, can be mathematically expressed by the same mathematical 9-D complex field expression, in a unifying way at which the physical determinism holds for the individual objects at all micro-macro scales in our Universe.
Author: Sadegh Raeisi Publisher: ISBN: Category : Languages : en Pages : 88
Book Description
Recent advances in quantum technologies enabled us to make large quantum states and pushed towards examining quantum theory at the macroscopic level. However observation of quantum e ects at a macroscopic level still remains a demanding task. In this thesis we try to address one of the challenges and propose and explore some new solutions. One of the obstacles for observation of macroscopic quantum e ects is the sensitivity to the measurement resolution. For many different cases, it has been observed that the precision requirement for measuring quantum effects increases with the system size. We formalize this as a conjecture that for observation of macroscopic quantum effects, either the outcome precision or the control precision of the measurements has to increase with system size. This indicates that the complexity of macroscopic quantum measurement increases with the system size and sheds some lights on the quantum-to-classical transition at the macroscopic level. We also introduce a technique to go around the sensitivity problem for observation of micro-macro entanglement. We propose that using a unitary deamplification process, one can bring the system back to the microscopic level where the measurements are less demanding and quantum effects are easier to verify. As the unitary processes do not change the entanglement, this serves as a verification tool for micro-macro entanglement. We also explored the connection between quantum effects and thermodynamics of macroscopic quantum systems for two specific cases. For one, we investigated the effect of entanglement in composite bosons and Bose-Einstein condensation. We showed that as the state of the composite boson approaches a maximally entangled state, the condensation rate also approaches one. The other case we considered was heat-bath algorithmic cooling. We found the cooling limit of this class of thermodynamic transformations and showed that it decreases exponentially with the number of qubits. We also developed an entropic version of Mermin's inequality. Here the idea is to develop a tool to reveal the entanglement in many-body quantum systems based on the entropy of the measurement outcomes. We introduce a new inequality that holds for locally realistic models, yet can be violated with quantum measurements. One of the nice features of this inequality is that it can be violated maximally with quantum measurements. This resembles the GHZ paradox but for entropies of the measurement outcomes.
Author: Guenter Mahler Publisher: CRC Press ISBN: 9814463744 Category : Science Languages : en Pages : 474
Book Description
The point of departure of this book is a triad of themes: information theory, thermodynamics, and quantum mechanics. These are related: thermodynamics and quantum mechanics form the basis of quantum thermodynamics; information and quantum mechanics underly, inter alia, the notorious quantum measurement problem; and information and thermodynamics ha
Author: James Binney Publisher: Oxford University Press, USA ISBN: 0199688575 Category : Science Languages : en Pages : 408
Book Description
This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.
Author: K. Kong Wan
Author: K. Kong Wan
Author: Vlatko Vedral
Author: Mark Fannes
Author: Izumi Ojima
Author: Bernardo A. Huberman
Author: Stephen J. Gustafson
Author: Zoran Majkic
Author: Sadegh Raeisi
Author: Guenter Mahler
Author: James Binney