Quantum Versus Classical Mechanics And Integrability Problems
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Quantum Versus Classical Mechanics And Integrability Problems
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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
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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.
A Collection Of Articles On Physics And Others
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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.
Chaotic Behavior In Quantum Systems
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Author : Giulio Casati
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Chaotic Behavior In Quantum Systems written by Giulio Casati 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.
Six years ago, in June 1977, the first international conference on chaos in classical dynamical systems took place here in Como. For the first time, physicists, mathematicians, biologists, chemists, economists, and others got together to discuss the relevance of the recent progress in nonlinear classical dynamics for their own research field. Immediately after, pUblication of "Nonlinear Science Abstracts" started, which, in turn, led to the Physica D Journal and to a rapid increase of the research activity in the whole area with the creation of numerous "Nonlinear Centers" around the world. During these years great progress has been made in understanding the qualitative behavior of classical dynamical systems and now we can appreciate the beautiful complexity and variety of their motion. Meanwhile, an increasing number of scientists began to wonder whether and how such beautiful structures would persist in quantum motion. Indeed, mainly integrable systems have been previously con sidered by Quantum Mechanics and therefore the problem is open how to describe the qualitative behavior of systems whose classical limit is non-integrable. The present meeting was organized in view of the fact that scientists working in different fields - mathematicians, theoretical physicists, solid state physicists, nuclear physicists, chemists and others - had common problems. Moreover, we felt that it was necessary to clarify some fundamental questions concerning the logical basis for the discussion including the very definition of chaos in Quantum Mechanics.
A Collection Of Papers On Chaos Theory And Its Applications
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Author : Paul Bracken
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-04-14
A Collection Of Papers On Chaos Theory And Its Applications written by Paul Bracken and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-14 with Mathematics categories.
This current volume contains 12 new papers on the subject of chaos in the physical sciences, which was initiated with the publication of the book Research Advances in Chaos Theory. It is clear the subject continues to attract a great deal of attention among scientists in the scientific community. This volume looks at such problems as chaos in nonlinear systems, in dynamical systems, quantum chaos, biological applications, and a few new emerging areas as well.
Classical Mechanics
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Author : Govind S. Krishnaswami
language : en
Publisher: Springer Nature
Release Date : 2025-08-31
Classical Mechanics written by Govind S. Krishnaswami and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-31 with Science categories.
This well-rounded and self-contained treatment of classical mechanics strikes a balance between examples, concepts, phenomena and formalism. While addressed to graduate students and their teachers, the minimal prerequisites and ground covered should make it useful also to undergraduates and researchers. Starting with conceptual context, physical principles guide the development. Chapters are modular and the presentation is precise yet accessible, with numerous remarks, footnotes and problems enriching the learning experience. Essentials such as Galilean and Newtonian mechanics, the Kepler problem, Lagrangian and Hamiltonian mechanics, oscillations, rigid bodies and motion in noninertial frames lead up to discussions of canonical transformations, angle-action variables, Hamilton-Jacobi and linear stability theory. Bifurcations, nonlinear and chaotic dynamics as well as the wave, heat and fluid equations receive substantial coverage. Techniques from linear algebra, differential equations, manifolds, vector and tensor calculus, groups, Lie and Poisson algebras and symplectic and Riemannian geometry are gently introduced. A dynamical systems viewpoint pervades the presentation. A salient feature is that classical mechanics is viewed as part of the wider fabric of physics with connections to quantum, thermal, electromagnetic, optical and relativistic physics highlighted. Thus, this book will also be useful in allied areas and serve as a stepping stone for embarking on research.
Symmetries And Integrability Of Difference Equations
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Author : Peter A. Clarkson
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-04
Symmetries And Integrability Of Difference Equations written by Peter A. Clarkson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-04 with Mathematics categories.
This volume comprises state-of-the-art articles in discrete integrable systems.
Energy Research Abstracts
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Author :
language : en
Publisher:
Release Date : 1994-12
Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12 with Power resources categories.
Quantum Integrable Systems
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Author : Asesh Roy Chowdhury
language : en
Publisher: CRC Press
Release Date : 2004-01-28
Quantum Integrable Systems written by Asesh Roy Chowdhury and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-28 with Science categories.
The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Integrable Hamiltonian Hierarchies
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Author : Vladimir Gerdjikov
language : en
Publisher: Springer
Release Date : 2008-12-02
Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-02 with Science categories.
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.