Download or read book Classical Analogies in the Solution of Quantum Many Body Problems written by Aydın Cem Keser and published by Springer. This book was released on 2018-11-07 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses problems in three main developments in modern condensed matter physics– namely topological superconductivity, many-body localization and strongly interacting condensates/superfluids–by employing fruitful analogies from classical mechanics. This strategy has led to tangible results, firstly in superconducting nanowires: the density of states, a smoking gun for the long sought Majorana zero mode is calculated effortlessly by mapping the problem to a textbook-level classical point particle problem. Secondly, in localization theory even the simplest toy models that exhibit many-body localization are mathematically cumbersome and results rely on simulations that are limited by computational power. In this book an alternative viewpoint is developed by describing many-body localization in terms of quantum rotors that have incommensurate rotation frequencies, an exactly solvable system. Finally, the fluctuations in a strongly interacting Bose condensate and superfluid, a notoriously difficult system to analyze from first principles, are shown to mimic stochastic fluctuations of space-time due to quantum fields. This analogy not only allows for the computation of physical properties of the fluctuations in an elegant way, it sheds light on the nature of space-time. The book will be a valuable contribution for its unifying style that illuminates conceptually challenging developments in condensed matter physics and its use of elegant mathematical models in addition to producing new and concrete results.
Download or read book Quantum Classical Analogies written by Daniela Dragoman and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.
Download or read book The Many Body Problem in Quantum Mechanics written by Norman Henry March and published by Courier Corporation. This book was released on 1995-01-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Single-volume account of methods used in dealing with the many-body problem and the resulting physics. Single-particle approximations, second quantization, many-body perturbation theory, Fermi fluids, superconductivity, many-boson systems, more. Each chapter contains well-chosen problems. Only prerequisite is basic understanding of elementary quantum mechanics. 1967 edition.
Download or read book Many Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
Download or read book Integrability Supersymmetry and Coherent States written by Şengül Kuru and published by Springer. This book was released on 2019-07-12 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.
Download or read book Classical and Quantum Dissipative Systems written by Mohsen Razavy and published by World Scientific. This book was released on 2006-01-17 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses issues associated with the quantum mechanical formulation of dissipative systems. It begins with an introductory review of phenomenological damping forces, and the construction of the Lagrangian and Hamiltonian for the damped motion. It is shown, in addition to these methods, that classical dissipative forces can also be derived from solvable many-body problems. A detailed discussion of these derived forces and their dependence on dynamical variables is also presented. The second part of this book investigates the use of classical formulation in the quantization of dynamical systems under the influence of dissipative forces. The results show that, while a satisfactory solution to the problem cannot be found, different formulations represent different approximations to the complete solution of two interacting systems. The third and final part of the book focuses on the problem of dissipation in interacting quantum mechanical systems, as well as the connection of some of these models to their classical counterparts. A number of important applications, such as the theory of heavy-ion scattering and the motion of a radiating electron, are also discussed. Contents:Phenomenological Equations of Motion for Dissipative SystemsLagrangian FormulationsHamiltonian FormulationHamilton-Jacobi FormulationMotion of a Charged Particle in an External Electromagnetic Field in the Presence of DampingNoether and Non-Noether Symmetries and Conservation LawsDissipative Forces Derived from Many-Body ProblemsA Particle Coupled to a FieldDamped Motion of the Central ParticleClassical Microscopic Models of Dissipation and Minimal Coupling RuleQuantization of Dissipative SystemsQuantization of Explicitly Time-Dependent HamiltonianDensity Matrix and the Wigner Distribution FunctionPath Integral Formulation of a Damped Harmonic OscillatorQuantization of the Motion of an Infinite ChainThe Heisenberg Equations of Motion for a Particle Coupled to a Heat BathQuantum Mechanical Models of Dissipative SystemsMore on the Concept of Optical Potential Readership: Researchers and graduate students in applied mathematics and theoretical physics. Key Features:Extensive treatment of the Hamiltonian formulation of the damped systemCoverage of a large number of solvable models, classical and quantum mechanical, which exhibit irreversibilityDetailed discussion of classical-quantal correspondenceIncludes discussion on motion of a charged particle in a viscous medium in the presence of an external electromagnetic field and the rule of minimal couplingKeywords:Classical and Quantum Dynamics of Damped Systems
Download or read book Exploring Classical Mechanics written by G. L. Kotkin and published by Oxford University Press. This book was released on 2020-08-10 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of a popular textbook offers an original collection of problems in analytical mechanics. Analytical mechanics is the first chapter in the study and understanding of theoretical physics. Its methods and ideas are crucially important, as they form the basis of all other branches of theoretical physics, including quantum mechanics, statistical physics, and field theory. Such concepts as the Lagrangian and Hamiltonian formalisms, normal oscillations, adiabatic invariants, Liouville theorem, and canonical transformations lay the foundation, without which any further in-depth study of theoretical physics is impossible. Wherever possible, the authors draw analogies and comparisons with similar processes in electrodynamics, quantum mechanics, or statistical mechanics while presenting the solutions to the problems. The book is based on the authors' many years of experience delivering lectures and seminars at the Department of Physics at Novosibirsk State University — totalling an impressive 110+ years of combined teaching experience. Most of the problems are original, and will be useful not only for those studying mechanics, but also for those who teach it. The content of the book corresponds to and roughly follows the mechanics course in the well-known textbooks by Landau and Lifshitz, Goldstein, or ter Haar. The Collection... starts with the Newtonian equations, motion in a central field, and scattering. Then the text proceeds to the established, traditional sections of analytical mechanics as part of the course on theoretical physics: the Lagrangian equations, the Noether theorem, linear and nonlinear oscillations, Hamilton formalism, and motion of a solid body. As a rule, the solution of a problem is not complete by just obtaining the required formulae. It's necessary to analyse the result. This can be an interesting process of discovery for the student and is by no means a "mechanical'' part of the solution. It is also very useful to investigate what happens if the conditions of the problem are varied. With this in mind, the authors offer suggestions of further problems at the end of several solutions. First published in 1969 in Russian, this text has become widely used in classrooms around the world. It has been translated into several languages, and has seen multiple editions in various languages.
Download or read book Quantum Many body Problems and Representation Theory written by Ivan Cherednik and published by . This book was released on 1998 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exploring Quantum Mechanics written by Viktor Mikhaĭlovich Galit︠s︡kiĭ and published by Oxford University Press. This book was released on 2013-02-28 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique resource on quantum physics that contains original problems with solutions that can be used by teachers and students of quantum mechanics at graduate and undergraduate level. Numerous tricks-of-the-trade in solving quantum physics problems are included which can also be used by professional researchers in all fields of modern physics.
Download or read book Solutions Manual for Quantum Mechanics written by Richard W. Robinett and published by Oxford University Press, USA. This book was released on 1997 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the familiar aspects of non-relativistic quantum mechanics were developed almost three quarters of a century ago, but the central role played by quantum physics in determining the properties of matter guarantees that new applications of the basic principles will continue to appear. Because the phenomena described by quantum theory are often remote from our daily existence, our intuition about the nature of quantum systems must be built up from sources other than direct experience; the visual display of quantitative information and qualitative ideas can play just as important a role in this learning process as do formal mathematical methods.Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples provides the student with a thorough background in the machinery of undergraduate quantum mechanics, with many examples taken from classic experiments in atomic, nuclear, and elementary particle physics. In addition, the use of visualization is heavily emphasized throughout.The text also includes several other valuable features:* Emphasis on the classical limit of quantum mechanics and wavepackets* Enhanced presentation of momentum-space methods* Increased emphasis on numerical and approximation techniques* Separate chapters on classical wave phenomena and probability/statistics to provide needed background, as well as an appendix on classical Hamiltonian theory* A chapter devoted to two-dimensional quantum systems, designed to make contact with modern surface physics; this includes a brief discussion of classical and quantum chaos* Many problems as well as questions in which the student is asked to explore more conceptual aspects of the mind
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 1132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applying Mathematics written by Otávio Bueno and published by Oxford University Press. This book was released on 2018-05-24 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otávio Bueno and Steven French offer a middle way, which focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics, which is formulated in terms of immersion, inference, and interpretation. In particular, the roles of idealisations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasize the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics, and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.
Download or read book The Many body Problem written by Daniel Charles Mattis and published by World Scientific. This book was released on 1993 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space ? such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz ? can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
Download or read book The Kinetic Theory of Gases written by Stephen G Brush and published by World Scientific. This book was released on 2003-07-28 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces physics students and teachers to the historical development of the kinetic theory of gases, by providing a collection of the most important contributions by Clausius, Maxwell and Boltzmann, with introductory surveys explaining their significance. In addition, extracts from the works of Boyle, Newton, Mayer, Joule, Helmholtz, Kelvin and others show the historical context of ideas about gases, energy and irreversibility. In addition to five thematic essays connecting the classical kinetic theory with 20th century topics such as indeterminism and interatomic forces, there is an extensive international bibliography of historical commentaries on kinetic theory, thermodynamics, etc. published in the past four decades. The book will be useful to historians of science who need primary and secondary sources to be conveniently available for their own research and interpretation, along with the bibliography which makes it easier to learn what other historians have already done on this subject. Contents:The Nature of Gases and of Heat (Boyle, Newton, Bernoulli, Gregory, Mayer, Joule, von Helmholtz, Clausius, Maxwell)Irreversible Processes (Maxwell, Boltzmann, Thomson, Poincaré, Zermelo)Historical Discussions by Stephen G BrushA Guide to Historical Commentaries: Kinetic Theory of Gases, Thermodynamics, and Related Topics Readership: Graduate and research students, teachers, lecturers and historians of physics. Keywords:Kinetic Theory;Gases;Boyle's Law;Gas Laws;Viscosity;Diffusion;Forces between Atoms and Molecules;Interatomic Forces;Ergodic Theorem;Ergodicity;Heat Conduction;Irreversibility;Indeterminism;Thermodynamics;First Law of Thermodynamics;Second Law of Thermodynamics;Third Law of Thermodynamics;Law of Conservation of Energy;Maxwell Velocity Distribution;Boltzmann's H Theorem;Boltzmann's (Transport) Equation;Reversibility Paradox;Recurrence Paradox;Statistical MechanicsReviews:“One of the most important contributions of this volume is the bibliography in Part IV … This is a useful book and should be on the shelves of all kinetic theorists and statistical mechanics.” Journal of Statistical Physics “This book will be useful both for historical research and for students studying the history of physics.”Notes and Records of the Royal Society “It is valuable to have the work in print again, since some of the originals are not always easily accessible and all who have struggled, for example, with Boltzmann's German will welcome accurate translations … The whole book is to be welcomed as an aid to those undertaking research or otherwise interested in exploring these fields.”AMBIX
Download or read book Modeling and Computational Methods for Kinetic Equations written by Pierre Degond and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Download or read book Mechanics written by T. T. Taylor and published by Elsevier. This book was released on 2016-10-13 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics: Classical and Quantum is a 13-chapter book that begins by explaining the Lagrangian and Hamiltonian formulation of mechanics. The Hamilton-Jacobi theory, historical background of the quantum theory, and wave mechanics are then described. Subsequent chapters discuss the time-independent Schrödinger equation and some of its applications; the operators, observables, and the quantization of a physical system; the significance of expectation values; and the concept of measurement in quantum mechanics. The matrix mechanics and the "hydrogenic atom", an atom in which one electron moves under the influence of a nucleus of charge that, to a very good approximation, can be thought of as a point, are also presented. This book will be very useful to students studying this field of interest.
