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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.
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.
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.
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.
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.
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.
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.
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.