Classical Analogies In The Solution Of Quantum Many Body Problems
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Classical Analogies In The Solution Of Quantum Many Body Problems
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Author : Aydın Cem Keser
language : en
Publisher: Springer
Release Date : 2018-11-07
Classical Analogies In The Solution Of Quantum Many Body Problems written by Aydın Cem Keser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-07 with Technology & Engineering categories.
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.
Quantum Classical Analogies
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Author : Daniela Dragoman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Quantum Classical Analogies written by Daniela Dragoman 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.
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.
The Many Body Problem In Quantum Mechanics
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Author : Norman Henry March
language : en
Publisher: Courier Corporation
Release Date : 1995-01-01
The Many Body Problem In Quantum Mechanics written by Norman Henry March and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Science categories.
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.
Exploring Classical Mechanics
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Author : Full Professor and Chair of Theoretical Physics G L Kotkin
language : en
Publisher: Oxford University Press, USA
Release Date : 2020-08
Exploring Classical Mechanics written by Full Professor and Chair of Theoretical Physics G L Kotkin and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08 with categories.
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.
Solutions Manual For Quantum Mechanics
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Author : Richard W. Robinett
language : en
Publisher: Oxford University Press, USA
Release Date : 1997
Solutions Manual For Quantum Mechanics written by Richard W. Robinett and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Quantum theory categories.
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
Exploring Quantum Mechanics
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Author : Viktor Mikhaĭlovich Galit︠s︡kiĭ
language : en
Publisher: Oxford University Press
Release Date : 2013-02-28
Exploring Quantum Mechanics written by Viktor Mikhaĭlovich Galit︠s︡kiĭ and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Science categories.
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.
Integrability Supersymmetry And Coherent States
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Author : Şengül Kuru
language : en
Publisher: Springer
Release Date : 2019-07-12
Integrability Supersymmetry And Coherent States written by Şengül Kuru and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Science categories.
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.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1973
Nuclear Science 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 1973 with Nuclear energy categories.
Applying Mathematics
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Author : Otávio Bueno
language : en
Publisher: Oxford University Press
Release Date : 2018-05-24
Applying Mathematics written by Otávio Bueno and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-24 with Science categories.
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.
The Many Body Problem
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Author : Daniel Charles Mattis
language : en
Publisher: World Scientific
Release Date : 1993
The Many Body Problem written by Daniel Charles Mattis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
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.