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Quantum Physics In One Dimension

Author: Thierry Giamarchi
Publisher: Oxford University Press
ISBN: 0198525001
Size: 13.77 MB
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This volume presents in a pedagogical yet complete way correlated systems in one dimension. After an introduction to the basic concepts of correlated systems, it gives a step-by-step description of the techniques needed to treat one dimension, and discusses the resulting physics.

Fundamentals Of The Physics Of Solids

Author: Jenö Sólyom
Publisher: Springer Science & Business Media
ISBN: 9783642045189
Size: 18.82 MB
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This book is the third of a three-volume series written by the same author. It aims to deliver a comprehensive and self-contained account of the fundamentals of the physics of solids. In the presentation of the properties and experimentally observed phenomena together with the basic concepts and theoretical methods, it goes far beyond most classic texts. The essential features of various experimental techniques are also explained. This volume is devoted mostly to the discussion of the effects of electron—electron interaction beyond the one-electron approximation. The density-functional theory is introduced to account for correlation effects. The response to external perturbations is discussed in the framework of linear response theory. Landau’s Fermi-liquid theory is followed by the theory of Luttinger liquids. The subsequent chapters are devoted to electronic phases with broken symmetry: to itinerant magnetism, to spin- and charge-density waves and their realizations in quasi-one-dimensional materials, as well as to the microscopic theory of superconductivity. An overview is given of the physics of strongly correlated systems. The last chapter covers selected problems in the physics of disordered systems.

Multi Species Systems In Optical Lattices

Author: Fernanda Pinheiro
Publisher: Springer
ISBN: 3319434640
Size: 74.12 MB
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This highly interdisciplinary thesis covers a wide range of topics relating to the interface of cold atoms, quantum simulation, quantum magnetism and disorder. With a self-contained presentation, it provides a broad overview of the rapidly evolving area of cold atoms and is of interest to both undergraduates and researchers working in the field. Starting with a general introduction to the physics of cold atoms and optical lattices, it extends the theory to that of systems with different multispecies atoms. It advances the theory of many-body quantum systems in excited bands (of optical lattices) through an extensive study of the properties of both the mean-field and strongly correlated regimes. Particular emphasis is given to the context of quantum simulation, where as shown here, the orbital degree of freedom in excited bands allows the study of exotic models of magnetism not easily achievable with the previous alternative systems. In addition, it proposes a new model Hamiltonian that serves as a quantum simulator of various disordered systems in different symmetry classes that can easily be reproduced experimentally. This is of great interest, especially for the study of disorder in 2D quantum systems.

Topological Phase Transitions And New Developments

Author: Jose Jorge V
Publisher: World Scientific
ISBN: 9813271353
Size: 47.89 MB
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Geometry and topology have been a fascination in physics since the start of the 20th century. A leading example is Einstein's geometrical theory of gravity. At the beginning of the 1970s, topological ideas entered areas of condensed matter physics. These advances were driven by new seminal ideas resolving a serious contradiction between experiment and the standard interpretation of a rigorous mathematical theorem which led to the study of new exotic topological phases of matter. Topological defect driven phase transitions in thin, two dimensional films of superfluids, superconductors and crystals have provided great insight into the mechanism governing these topological phases present in those physical systems. Moreover, many of these topological properties remain 'protected' against disorder and topological distortion perturbations. An example of possible applications of such robustness to perturbations is in the search for encoding information in quantum computers, potentially providing the platform for fault-tolerant quantum computations. In the past four decades, the discovery of topological phases engendered great interest in condensed matter physics. It also attracted the attention of researchers working on quantum information, quantum materials and simulations, high energy physics and string theory. This unique volume contains articles written by some of the most prominent names in the field, including Nobel Laureate John Michael Kosterlitz and Professor Jorge V José. They originate from talks and discussions by leading experts at a recent workshop. They review previous works as well as addressing contemporary developments in the most pressing and important issues on various aspects of topological phases and topological phase transitions.

Klassische Mechanik

Author: Herbert Goldstein
Publisher: John Wiley & Sons
ISBN: 3527662073
Size: 70.60 MB
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Der Goldstein gehört zu den Standardwerken für die Vorlesung in Klassischer Mechanik, die Pflichtvorlesung und Teil des Theorie-Lehrplans jedes Physik-Studienganges ist. Für diese aktuelle Ausgabe haben Charles Poole und John Safko die Texte überarbeitet und neueste Themen, Anwendungen und Notationen eingearbeitet und sind damit auf moderne Trends in der Theoretischen Mechanik eingegangen. Neue numerische Übungen verhelfen den Studenten zur Fähigkeit, Computeranwendungen für die Lösung von Physikproblemen zu benutzen. Mathematische Techniken werden detailliert eingeführt, so daß der Text auch für Studenten ohne den entsprechenden Hintergrund der Theoretischen Mechanik verständlich ist.

Anomalies In Quantum Field Theory

Author: Reinhold A. Bertlmann
Publisher: Oxford University Press
ISBN: 9780198507628
Size: 63.27 MB
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An anomaly is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper understanding of quantum field theory and has played an increasingly important role in the theory over the past 20 years. This text presents all the different aspects of the study of anomalies in an accessible and self-contained way. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. This approach is followed here, and the derivations and calculations are given explicitly as an aid to students. Topics discussed include the relevant ideas from differential geometry and topology and the application of these paths (path integrals, differential forms, homotopy operators, etc.) to the study of anomalies. Chapters are devoted to abelian and nonabelian anomalies, consistent and covariant anomalies, and gravitational anomalies. The comprehensive overview of the theory presented in this book will be useful to both students and researchers.

An Introduction To Non Perturbative Foundations Of Quantum Field Theory

Author: Franco Strocchi
Publisher: OUP Oxford
ISBN: 0191651346
Size: 30.62 MB
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Quantum Field Theory (QFT) has proved to be the most useful strategy for the description of elementary particle interactions and as such is regarded as a fundamental part of modern theoretical physics. In most presentations, the emphasis is on the effectiveness of the theory in producing experimentally testable predictions, which at present essentially means Perturbative QFT. However, after more than fifty years of QFT, we still are in the embarrassing situation of not knowing a single non-trivial (even non-realistic) model of QFT in 3+1 dimensions, allowing a non-perturbative control. As a reaction to these consistency problems one may take the position that they are related to our ignorance of the physics of small distances and that QFT is only an effective theory, so that radically new ideas are needed for a consistent quantum theory of relativistic interactions (in 3+1 dimensions). The book starts by discussing the conflict between locality or hyperbolicity and positivity of the energy for relativistic wave equations, which marks the origin of quantum field theory, and the mathematical problems of the perturbative expansion (canonical quantization, interaction picture, non-Fock representation, asymptotic convergence of the series etc.). The general physical principles of positivity of the energy, Poincare' covariance and locality provide a substitute for canonical quantization, qualify the non-perturbative foundation and lead to very relevant results, like the Spin-statistics theorem, TCP symmetry, a substitute for canonical quantization, non-canonical behaviour, the euclidean formulation at the basis of the functional integral approach, the non-perturbative definition of the S-matrix (LSZ, Haag-Ruelle-Buchholz theory). A characteristic feature of gauge field theories is Gauss' law constraint. It is responsible for the conflict between locality of the charged fields and positivity, it yields the superselection of the (unbroken) gauge charges, provides a non-perturbative explanation of the Higgs mechanism in the local gauges, implies the infraparticle structure of the charged particles in QED and the breaking of the Lorentz group in the charged sectors. A non-perturbative proof of the Higgs mechanism is discussed in the Coulomb gauge: the vector bosons corresponding to the broken generators are massive and their two point function dominates the Goldstone spectrum, thus excluding the occurrence of massless Goldstone bosons. The solution of the U(1) problem in QCD, the theta vacuum structure and the inevitable breaking of the chiral symmetry in each theta sector are derived solely from the topology of the gauge group, without relying on the semiclassical instanton approximation.

Bose Einstein Condensation

Author: Lev. P. Pitaevskii
Publisher: Oxford University Press
ISBN: 9780198507192
Size: 25.94 MB
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Bose-Einstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 Nobel Prize. Providing a useful introduction to one of the most exciting fields of physics today, this text will be of interest to a growing community of physicists, and is easily accessible to non-specialists alike.