Quantum Versus Classical Mechanics And Integrability Problems

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Quantum versus Classical Mechanics and Integrability Problems

Maciej Błaszak
Quantum versus Classical Mechanics and Integrability Problems Book PDF

Author : Maciej Błaszak
Publisher : Springer
Page : 460 pages
File Size : 44,9 Mb
Release : 2019-06-11
Category : Science
ISBN : 9783030183790

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Quantum versus Classical Mechanics and Integrability Problems by Maciej Błaszak Pdf

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

Maciej BÅ‚aszak
Quantum Versus Classical Mechanics and Integrability Problems Book PDF

Author : Maciej BÅ‚aszak
Publisher : Unknown
Page : 460 pages
File Size : 51,8 Mb
Release : 2019
Category : Mechanics
ISBN : 3030183807

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Quantum Versus Classical Mechanics and Integrability Problems by Maciej BÅ‚aszak Pdf

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

Jin Tong Wang Ph. D
A Collection of Articles on Physics and Others Book PDF

Author : Jin Tong Wang Ph. D
Publisher : Xlibris Corporation
Page : 418 pages
File Size : 49,5 Mb
Release : 2022-08-14
Category : Biography & Autobiography
ISBN : 9781669813644

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A Collection of Articles on Physics and Others by Jin Tong Wang Ph. D Pdf

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.

Elements of Classical and Quantum Integrable Systems

Gleb Arutyunov
Elements of Classical and Quantum Integrable Systems Book PDF

Author : Gleb Arutyunov
Publisher : Springer
Page : 414 pages
File Size : 42,9 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

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Elements of Classical and Quantum Integrable Systems by Gleb Arutyunov Pdf

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 Systems, Quantum Groups, and Quantum Field Theories

Alberto Ibort,M.A. Rodríguez
Integrable Systems Quantum Groups and Quantum Field Theories Book PDF

Author : Alberto Ibort,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401119801

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Integrable Systems, Quantum Groups, and Quantum Field Theories by Alberto Ibort,M.A. Rodríguez Pdf

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.

Classical and Quantum Mechanics of Noncentral Potentials

Radhey S. Kaushal
Classical and Quantum Mechanics of Noncentral Potentials Book PDF

Author : Radhey S. Kaushal
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 47,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662113257

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Classical and Quantum Mechanics of Noncentral Potentials by Radhey S. Kaushal Pdf

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.

Quantum Theory, Deformation and Integrability

R. Carroll
Quantum Theory Deformation and Integrability Book PDF

Author : R. Carroll
Publisher : Elsevier
Page : 420 pages
File Size : 42,8 Mb
Release : 2000-11-09
Category : Science
ISBN : 0080540082

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Quantum Theory, Deformation and Integrability by R. Carroll Pdf

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.

Chaos in Classical and Quantum Mechanics

Martin C. Gutzwiller
Chaos in Classical and Quantum Mechanics Book PDF

Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 55,9 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461209836

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Chaos in Classical and Quantum Mechanics by Martin C. Gutzwiller Pdf

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.

Quantum-Classical Correspondence

A. O. Bolivar
Quantum Classical Correspondence Book PDF

Author : A. O. Bolivar
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 48,9 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096499

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Quantum-Classical Correspondence by A. O. Bolivar Pdf

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 Many-particle Systems

Vladimir Inozemtsev
Integrable Many particle Systems Book PDF

Author : Vladimir Inozemtsev
Publisher : World Scientific
Page : 267 pages
File Size : 54,6 Mb
Release : 2023-04-25
Category : Science
ISBN : 9781800613836

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Integrable Many-particle Systems by Vladimir Inozemtsev Pdf

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 Integrable Systems

Asesh Roy Chowdhury,Aninlya Ghose Choudhury
Quantum Integrable Systems Book PDF

Author : Asesh Roy Chowdhury,Aninlya Ghose Choudhury
Publisher : CRC Press
Page : 425 pages
File Size : 52,9 Mb
Release : 2004-01-28
Category : Science
ISBN : 9780203498019

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Quantum Integrable Systems by Asesh Roy Chowdhury,Aninlya Ghose Choudhury Pdf

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

Quantum Mechanics for Mathematicians

Leon Armenovich Takhtadzhi͡an
Quantum Mechanics for Mathematicians Book PDF

Author : Leon Armenovich Takhtadzhi͡an
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 43,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846308

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Quantum Mechanics for Mathematicians by Leon Armenovich Takhtadzhi͡an Pdf

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.

Advanced Quantum Mechanics

Reinhold Blumel
Advanced Quantum Mechanics Book PDF

Author : Reinhold Blumel
Publisher : Jones & Bartlett Publishers
Page : 437 pages
File Size : 43,7 Mb
Release : 2010-04-28
Category : Medical
ISBN : 9781449655907

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Advanced Quantum Mechanics by Reinhold Blumel Pdf

This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.

Foundations Of Quantum Mechanics, The: Historical Analysis And Open Questions

Claudio Garola,Arcangelo Rossi
Foundations Of Quantum Mechanics The Historical Analysis And Open Questions Book PDF

Author : Claudio Garola,Arcangelo Rossi
Publisher : World Scientific
Page : 436 pages
File Size : 41,7 Mb
Release : 2000-05-11
Category : Science
ISBN : 9789814493383

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Foundations Of Quantum Mechanics, The: Historical Analysis And Open Questions by Claudio Garola,Arcangelo Rossi Pdf

This volume provides a sample of the present research on the foundations of quantum mechanics and related topics by collecting the papers of the Italian scholars who attended the conference entitled “The Foundations of Quantum Mechanics — Historical Analysis and Open Questions” (Lecce, 1998). The perspective of the book is interdisciplinary, and hence philosophical, historical and technical papers are gathered together so as to allow the reader to compare different viewpoints and cultural approaches. Most of the papers confront, directly or indirectly, the objectivity problem, taking into account the positions of the founders of QM or more recent developments. More specifically, the technical papers in the book pay special attention to the interpretation of the experiments on Bell's inequalities and to decoherence theory, but topics on unsharp QM, the consistent-history approach, quantum probability and alternative theories are also discussed. Furthermore, a number of historical and philosophical papers are devoted to Planck's, Weyl's and Pauli's thought, but topics such as quantum ontology, predictivity of quantum laws, etc., are treated.

Classical Nonintegrability, Quantum Chaos

Andreas Knauf,Yakov G. Sinai
Classical Nonintegrability Quantum Chaos Book PDF

Author : Andreas Knauf,Yakov G. Sinai
Publisher : Springer Science & Business Media
Page : 114 pages
File Size : 49,9 Mb
Release : 1997-03-20
Category : Science
ISBN : 3764357088

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Classical Nonintegrability, Quantum Chaos by Andreas Knauf,Yakov G. Sinai Pdf

Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.