Quantum Versus Classical Mechanics And Integrability Problems

Author : Maciej Błaszak
Publisher : Springer
ISBN 13 : 3030183793
Total Pages : 460 pages
Book Rating : 4.90/5 ( download)

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Download or read book Quantum versus Classical Mechanics and Integrability Problems written by Maciej Błaszak and published by Springer. This book was released on 2019-06-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

Author : Maciej BÅ‚aszak
Publisher :
ISBN 13 : 9783030183806
Total Pages : 460 pages
Book Rating : 4.07/5 ( download)

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Download or read book Quantum Versus Classical Mechanics and Integrability Problems written by Maciej Błaszak and published by . This book was released on 2019 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author. The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language. In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy. The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations. The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories. In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas. Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

Author : Gleb Arutyunov
Publisher : Springer
ISBN 13 : 303024198X
Total Pages : 414 pages
Book Rating : 4.88/5 ( download)

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Download or read book Elements of Classical and Quantum Integrable Systems written by Gleb Arutyunov and published by Springer. This book was released on 2019-07-23 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Author : Jin Tong Wang Ph. D
Publisher : Xlibris Corporation
ISBN 13 : 1669813649
Total Pages : 418 pages
Book Rating : 4.44/5 ( download)

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Download or read book A Collection of Articles on Physics and Others written by Jin Tong Wang Ph. D and published by Xlibris Corporation. This book was released on 2022-08-14 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about Dr. Jin Tong Wang’s collected research works included: 1) Brillouin “Small Angle, Right Angle and Backscattering”. There were achieved three significances, a) smallest angle scattering in the world at that time. It was a world record; b) discovered from small angle, right angle and backscattering results, the sound velocity was not a constant with the same phonon mode. It actually depends on the phone frequencies. At that time, no one in this field didn’t know how to interpret it. Based on the results in the study, published a paper in Physical Review B in 1986; 2) By the support of Office of Naval Research, we created quite a few navel Ferro-piezoelectric materials. We have done experiments on ferroelectricity, piezoelectricity and pyroelectricity measurements. Based on the experiment we have some intriguing findings; 3) We also work on theories on several topics. First of all, we proposed a displacive- order-disorder (DOD) ferroelectric transition model for para-ferroelectric phase transition mechanism. The paper was published in the well-known European journal “Ferroelectrics”. The DOD phase transition mechanism clarified the long-time dispute whether the para-ferroelectric phase transition was displacive or order-disorder one; 4) Derived an Accurate Formulation of Faraday, Magnetic Circular Dichroism (MCD) and Kerr Effect of Light in Ferro-electromagnet.; 5) published several papers in the frontier of quantum mechanics including: the red shift of photon frequency in gravitational potential; the mechanism of electron photo emission; the unification of classical mechanics and quantum mechanics; the origin of quantum particle entanglement and quantum wave packet tunneling. Some papers have caught attentions by physics communities; 5) two patents created by author. One is microwave-plasma and plasma torch gasifier. Another one is plasma torch directly refine metal titanium; 6) Also published some papers in Chinese. Some were appeared well-known Chinese News Paper. In some paper, the advantages and disadvantages in two social systems were analyzed in physical point of view. All these published papers are edited in this collection.

Author : Leon Armenovich Takhtadzhi͡an
Publisher : American Mathematical Soc.
ISBN 13 : 0821846302
Total Pages : 410 pages
Book Rating : 4.08/5 ( download)

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Download or read book Quantum Mechanics for Mathematicians written by Leon Armenovich Takhtadzhi͡an and published by American Mathematical Soc.. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.

Author : A. O. Bolivar
Publisher : Springer Science & Business Media
ISBN 13 : 3662096498
Total Pages : 196 pages
Book Rating : 4.99/5 ( download)

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Download or read book Quantum-Classical Correspondence written by A. O. Bolivar and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.

Author : Vladimir Inozemtsev
Publisher : World Scientific
ISBN 13 : 1800613830
Total Pages : 267 pages
Book Rating : 4.36/5 ( download)

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Download or read book Integrable Many-particle Systems written by Vladimir Inozemtsev and published by World Scientific. This book was released on 2023-04-25 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is commonly known that three or more particles interacting via a two-body potential is an intractable problem. However, similar systems confined to one dimension yield exactly solvable equations, which have seeded widely pursued studies of one-dimensional n-body problems. The interest in these investigations is justified by their rich and quantitative insights into real-world classical and quantum problems, birthing a field that is the subject of this book. Spanning four bulk chapters, this book is written with the hope that readers come to appreciate the beauty of the mathematical results concerning the models of many-particle systems, such as the interaction between light particles and infinitely massive particles, as well as interacting quasiparticles. As the book discusses several unsolved problems in the subject, it functions as an insightful resource for researchers working in this branch of mathematical physics.In Chapter 1, the author first introduces readers to interesting problems in mathematical physics, with the prime objective of finding integrals of motion for classical many-particle systems as well as the exact solutions of the corresponding equations of motions. For these studied systems, their quantum mechanical analogue is then developed in Chapter 2. In Chapter 3, the book focuses on a quintessential problem in the quantum theory of magnetism: namely, to find all integrable one-dimensional systems involving quasiparticles of interacting one-half spins. Readers will study the integrable periodic chains of interacting one-half spins and discover the integrals of motion for such systems, as well as the eigenvectors of their corresponding Hamiltonians. In the last chapter, readers will study about integrable systems of quantum particles, with spin and mutual interactions involving rational, trigonometric, or elliptic potentials.

Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
ISBN 13 : 1461209838
Total Pages : 445 pages
Book Rating : 4.36/5 ( download)

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Download or read book Chaos in Classical and Quantum Mechanics written by Martin C. Gutzwiller and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

Author : Alberto Ibort
Publisher : Springer Science & Business Media
ISBN 13 : 9401119805
Total Pages : 508 pages
Book Rating : 4.01/5 ( download)

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Download or read book Integrable Systems, Quantum Groups, and Quantum Field Theories written by Alberto Ibort and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

Author : R. Carroll
Publisher : Elsevier
ISBN 13 : 9780080540085
Total Pages : 420 pages
Book Rating : 4.82/5 ( download)

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Download or read book Quantum Theory, Deformation and Integrability written by R. Carroll and published by Elsevier. This book was released on 2000-11-09 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.