Band Theory and Electronic Properties of Solids

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Description This book provides an introduction to band theory and the electronic properties of materials at a level suitable for final-year undergraduates or first-year graduate students. It sets out to provide the vocabulary and quantum-mechanical training necessary to understand the electronic, optical and structural properties of the materials met in science and technology and describes some of the experimental techniques which are used to study band structure today. In order to leave space for recent developments, the Drude model and the introduction of quantum statistics are treated synoptically. However, Bloch's theorem and two tractable limits, a very weak periodic potential and the tight-binding model, are developed rigorously and in three dimensions. Having introduced the ideas of bands, effective masses and holes, semiconductor and metals are treated in some detail, along with the newer ideas of artificial structures such as super-lattices and quantum wells, layered organic substances and oxides. Some recent `hot topics' in research are covered, e.g. the fractional Quantum Hall Effect and nano-devices, which can be understood using the techniques developed in the book. In illustrating examples of e.g. the de Haas-van Alphen effect, the book focuses on recent experimental data, showing that the field is a vibrant and exciting one. References to many recent review articles are provided, so that the student can conduct research into a chosen topic at a deeper level. Several appendices treating topics such as phonons and crystal structure make the book self-contained introduction to the fundamentals of band theory and electronic properties in condensed matter physic today.

Fundamentals of Condensed Matter Physics (1版)

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Based on an established course and covering the fundamentals, central areas and contemporary topics of this diverse field, Fundamentals of Condensed Matter Physics is a much-needed textbook for graduate students. The book begins with an introduction to the modern conceptual models of a solid from the points of view of interacting atoms and elementary excitations. It then provides students with a thorough grounding in electronic structure and many-body interactions as a starting point to understand many properties of condensed matter systems - electronic, structural, vibrational, thermal, optical, transport, magnetic and superconducting - and methods to calculate them. Taking readers through the concepts and techniques, the text gives both theoretically and experimentally inclined students the knowledge needed for research and teaching careers in this field. It features 246 illustrations, 9 tables and 100 homework problems, as well as numerous worked examples, for students to test their understanding. Solutions to the problems for instructors are available at www.cambridge.org/cohenlouie.

Spin Glass Theory and Far Beyond

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About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew the attention of theoretical physicists. It soon became clear that understanding these systems, now called spin glasses, would give rise to a new branch of statistical physics. As physical materials, spin glasses were found to be as useless as they were exotic. They have nevertheless been recognized as paradigmatic examples of complex systems with applications to problems as diverse as neural networks, amorphous solids, biological molecules, social and economic interactions, information theory and constraint satisfaction problems. This book presents an encyclopaedic overview of the broad range of these applications. More than 30 contributions are compiled, written by many of the leading researchers who have contributed to these developments over the last few decades. Some timely and cutting-edge applications are also discussed. This collection serves well as an introduction and summary of disordered and glassy systems for advanced undergraduates, graduate students and practitioners interested in the topic. Sample Chapter(s) Preface Chapter 1: Simulated Annealing, Optimization, Searching for Ground States Chapter 34: Future Perspectives Contents: Simulated Annealing, Optimization, Searching for Ground States (Sergio Caracciolo, Alexander Hartmann, Scott Kirkpatrick and Martin Weigel) Beyond the Ising Spin Glass I: m-Vector, Potts, p-Spin, Spherical, Induced Moment, Random Graphs (David Sherrington and Jairo R L de Almeida) Beyond the Ising Spin Glass II: Spin Glass Without Replicas (J Michael Kosterlitz) Renormalization Group in Spin Glasses (Tom Lubensky, Tamás Temesvári, Imre Kondor and Maria Chiara Angelini) Numerical Simulations and Replica Symmetry Breaking (Víctor Martín-Mayor, Juan J Ruiz-Lorenzo, Beatriz Seoane and A Peter Young) The High-dimensional Landscape Paradigm: Spin-Glasses, and Beyond (Valentina Ros and Yan V Fyodorov) Universal Aspects of the Structural Glass Transition from Density Functional Theory (Theodore R Kirkpatrick and Dave Thirumalai) Non-Perturbative Processes in Glasses (Peter G Wolynes and Tommaso Rizzo) Dynamical Mean-Field Theory and the Aging Dynamics (Andrea Crisanti, Silvio Franz, Jorge Kurchan and Andrea Maiorano) Dynamical Heterogeneity in Glass-Forming Liquids (Giulio Biroli, Kunimasa Miyazaki and David R Reichman) The Kauzmann Transition to an Ideal Glass Phase (Chiara Cammarota, Misaki Ozawa and Gilles Tarjus) The Gardner Glass (Pierfrancesco Urbani, Yuliang Jin and Hajime Yoshino) The Jamming Transition and the Marginally Stable Solid (Francesco Arceri, Eric I Corwin and Corey S O'Hern) From Polymers to the KPZ Equation (Victor Dotsenko, Pierre Le Doussal and Henri Orland) Emergent Dynamics in Glasses and Disordered Systems: Correlations and Avalanches (Annette Zippelius, Matthias Fuchs, Alberto Rosso, James P Sethna and Matthieu Wyart) Replica Symmetry Breaking in Random Lasers: Experimental Measurement of the Overlap Distribution (Claudio Conti, Neda Ghofraniha, Luca Leuzzi and Giancarlo Ruocco) Anderson Localization on the Bethe Lattice (Saverio Pascazio, Antonello Scardicchio and Marco Tarzia) Quantum Glasses (Leticia F Cugliandolo and Markus Müller) The Cavity Method: From Exact Solutions to Algorithms (Alfredo Braunstein and Guilhem Semerjian) Message Passing and Its Applications (Florent Krzakala, Manfred Opper and David Saad) Information and Communication (Yoshiyuki Kabashima and Toshiyuki Tanaka) The Mighty Force: Statistical Inference and High-Dimensional Statistics (Erik Aurell, Jean Barbier, Aurélien Decelle and Roberto Mulet) Disordered Systems Insights on Computational Hardness (David Gamarnik, Cris Moore and Lenka Zdeborová) Neural Networks: From the Perceptron to Deep Nets (Marylou Gabrié, Surya Ganguli, Carlo Lucibello and Riccardo Zecchina) From the Statistical Physics of Disordered Systems to Neuroscience (Nicolas Brunel, Rémi Monasson, Haim Sompolinsky and J Leo van Hemmen) Statistical Physics of Biological Molecules (Simona Cocco, Andrea De Martino, Andrea Pagnani, Martin Weigt and Felix Ritort) Application of Spin Glass Ideas in Social Sciences, Economics and Finance (Jean-Philippe Bouchaud, Matteo Marsili and Jean-Pierre Nadal) Complex Dynamics in Ecological Systems and Animal Behavior (M Cristina Marchetti, Irene Giardina and A Altieri) Optimization of Random High-Dimensional Functions: Structure and Algorithms (Antonio Auffinger, Andrea Montanari and Eliran Subag) Rigorous Results in the Sherrington–Kirkpatrick Model (Wei-Kuo Chen, Dmitry Panchenko and Francesco Guerra) Random Energy Models: Broken Replica Symmetry and Activated Dynamics (Bernard Derrida, Peter Mottishaw and Véronique Gayrard) Rigorous Results: Random Constraint Satisfaction Problems (Amin Coja-Oghlan, Allan Sly and Nike Sun) Metastates and Replica Symmetry Breaking (C M Newman, N Read and D L Stein) Future Perspectives (Giorgio Parisi) Readership: Advanced undergraduate and graduate students, researchers and practitioners in the fields of statistical physics and its applications, with a particular focus on glassy and disordered systems, both classical and quantum, and computer science, ecological, biological and financial applications.

Advanced Topics in Quantum Mechanics (1版)

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Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout. Covers many advanced mathematical techniques in quantum mechanics, each illustrated with detailed examples Presents two alternative formulations of quantum mechanics; the path integral and phase space formulations, which are useful in advanced applications Provides a pedagogical and thorough overview of the exact WKB method, which plays an increasingly important role in many areas of modern physics