Quantum Versus Classical Mechanics And Integrability Problems
DOWNLOAD
Download Quantum Versus Classical Mechanics And Integrability Problems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Quantum Versus Classical Mechanics And Integrability Problems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Quantum Versus Classical Mechanics And Integrability Problems
DOWNLOAD
Author : Maciej Błaszak
language : en
Publisher: Springer
Release Date : 2019-06-11
Quantum Versus Classical Mechanics And Integrability Problems written by Maciej Błaszak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Science categories.
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.
Quantum Versus Classical Mechanics And Integrability Problems
DOWNLOAD
Author : Maciej BÅ‚aszak
language : en
Publisher:
Release Date : 2019
Quantum Versus Classical Mechanics And Integrability Problems written by Maciej BÅ‚aszak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mechanics categories.
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.
Elements Of Classical And Quantum Integrable Systems
DOWNLOAD
Author : Gleb Arutyunov
language : en
Publisher: Springer
Release Date : 2019-07-23
Elements Of Classical And Quantum Integrable Systems written by Gleb Arutyunov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Science categories.
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.
Integrable Many Particle Systems
DOWNLOAD
Author : Vladimir Inozemtsev
language : en
Publisher: World Scientific
Release Date : 2023-04-25
Integrable Many Particle Systems written by Vladimir Inozemtsev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-25 with Science categories.
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.
Quantum Classical Correspondence
DOWNLOAD
Author : A. O. Bolivar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Quantum Classical Correspondence written by A. O. Bolivar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.
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.
Integrable Systems Quantum Groups And Quantum Field Theories
DOWNLOAD
Author : Alberto Ibort
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Systems Quantum Groups And Quantum Field Theories written by Alberto Ibort and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Quantum Theory Deformation And Integrability
DOWNLOAD
Author : R. Carroll
language : en
Publisher: Elsevier
Release Date : 2000-11-09
Quantum Theory Deformation And Integrability written by R. Carroll and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-09 with Science categories.
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.
A Collection Of Articles On Physics And Others
DOWNLOAD
Author : Jin Tong Wang Ph. D
language : en
Publisher: Xlibris Corporation
Release Date : 2022-08-14
A Collection Of Articles On Physics And Others written by Jin Tong Wang Ph. D and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-14 with Biography & Autobiography categories.
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.
Quantum Non Integrability
DOWNLOAD
Author : Da-hsuan Feng
language : en
Publisher: World Scientific
Release Date : 1992-09-30
Quantum Non Integrability written by Da-hsuan Feng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-09-30 with categories.
Recent developments in nonlinear dynamics has significantly altered our basic understanding of the foundations of classical physics. However, it is quantum mechanics, not classical mechanics, which describes the motion of the nucleons, atoms, and molecules in the microscopic world. What are then the quantum signatures of the ubiquitous chaotic behavior observed in classical physics? In answering this question one cannot avoid probing the deepest foundations connecting classical and quantum mechanics. This monograph reviews some of the most current thinkings and developments in this exciting field of physics.
Classical And Quantum Mechanics Of Noncentral Potentials
DOWNLOAD
Author : Radhey S. Kaushal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Classical And Quantum Mechanics Of Noncentral Potentials written by Radhey S. Kaushal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
Non-central forces have a wide variety of applications in classical and quantum mechanics as demonstrated in this book. The author emphasizes the study of time-dependent potentials, predominantly in two dimensions, without neglecting the quite well understood time-independent case. The construction of invariants in the classical case and the study of solutions to Schrödinger's equation, as well as a detailed presentation of various mathematical techniques are of main concern to the author. The book addresses theoretical physicists and mathematicians, but it will also be useful for electrical and mechanical engineers.