| Description |
1 online resource (xi, 261 pages) : illustrations (some color) |
| Series |
Lecture notes in physics, 0075-8450 ; volume 934 |
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Lecture notes in physics ; 934. 0075-8450
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| Contents |
Intro -- Preface -- Contents -- 1 Perturbation Theory and Effective Hamiltonian -- 1.1 Projection onto Model Space -- 1.2 Rearrangement of Perturbation Series -- 1.3 Hydrogen Molecule -- 1.4 Oxygen Molecule -- 1.5 Itinerant vs. Localized Limits in a Molecule -- Problems -- Solutions to Problems -- References -- 2 Itinerant and Localized Characters of Electrons -- 2.1 Model of Electrons in Solids -- 2.2 Formation of Energy Bands -- 2.3 Localized Orbitals and Hopping of Electrons -- 2.4 Density of States of Electrons -- Problems -- Solutions to Problems -- References |
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3 Linear Response and Green Functions -- 3.1 Static Response -- 3.2 Dynamic Response -- 3.3 Green Function and Its Spectral Representation -- 3.4 Green Functions with Imaginary Time -- 3.5 Relaxation Function -- 3.6 Liouville Operator Formalism -- 3.7 Green Function for Fermions -- Problems -- Solutions to Problems -- References -- 4 Fermi Liquid Theory -- 4.1 Quasi-Particles and Their Distributions -- 4.2 Specific Heat and Magnetic Susceptibility -- 4.3 Dynamical Response of Fermi Liquid -- Problems -- Solutions to Problems -- References -- 5 Superconductivity -- 5.1 Breakdown of Gauge Symmetry |
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5.2 Attractive Interaction Mediated by Phonons -- 5.3 Mean Field Approximation -- 5.4 Multiband Model -- 5.5 Renormalization of Coulomb Repulsion -- 5.6 Isotope Effect -- 5.7 Spin Structure of Cooper Pairs -- 5.8 Anisotropic Cooper Pairs -- 5.9 Pairing with Repulsive Interaction -- Problems -- Solutions to Problems -- References -- 6 Kondo Effect -- 6.1 Hybridization and Exchange Interactions -- 6.2 Renormalization in Kondo Model -- 6.3 Anisotropic Kondo Model -- 6.4 Ground State of Kondo Systems -- 6.5 Local Fermi Liquid -- 6.6 Mean Field Theory for Kondo Systems |
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6.7 Dynamical Susceptibility of Kondo Impurity -- 6.8 Multi-Channel Kondo Model -- 6.9 Realization of Multi-Channel Kondo Systems -- 6.9.1 Orbital as Source of Channels -- 6.9.2 Spin as Source of Channels -- 6.9.3 Nano-Scale Reservoir as Source of Channels -- Problems -- Solutions to Problems -- References -- 7 One-Dimensional Fermions and Bosonization -- 7.1 Quantum Theory of String Oscillation -- 7.2 Bosonization of Free Fermi Gas -- 7.3 Bosonic Representation of Fermions -- 7.4 Inclusion of Forward Scattering -- 7.5 Momentum Distribution Near the Fermi Level |
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7.6 Separation of Spin and Charge -- 7.7 Backward and Umklapp Scatterings -- 7.8 Superconductivity and Mott Insulator -- 7.9 Kondo Effect Revisited -- 7.9.1 Bosonization and Fictitious Fermions in Kondo Model -- 7.9.2 Two-Channel Kondo Model -- Problems -- Solutions to Problems -- References -- 8 Fractionalization of Charge and Statistics -- 8.1 Magnetic Flux and Geometric Phase -- 8.2 Fractional Charge in Two Dimensions -- 8.3 Sutherland Model and Its Exact Eigenvalues -- 8.4 Rapidity of Quasi-Particles -- 8.5 Distribution Function and Entropy -- 8.6 Exclusion Statistics |
| Summary |
This book offers a compact tutorial on basic concepts and tools in quantum many-body physics, and focuses on the correlation effects produced by mutual interactions. The content is divided into three parts, the first of which introduces readers to perturbation theory. It begins with the simplest examples-hydrogen and oxygen molecules-based on their effective Hamiltonians, and looks into basic properties of electrons in solids from the perspective of localized and itinerant limits. Readers will also learn about basic theoretical methods such as the linear response theory and Green functions. The second part focuses on mean-field theory for itinerant electrons, e.g. the Fermi liquid theory and superconductivity. Coulomb repulsion among electrons is addressed in the context of high-Tc superconductivity in cuprates and iron pnictides. A recent discovery concerning hydride superconductors is also briefly reviewed. In turn, the third part highlights quantum fluctuation effects beyond the mean-field picture. Discussing the dramatic renormalization effect in the Kondo physics, it provides a clear understanding of nonperturbative interaction effects. Further it introduces readers to fractionally charged quasi-particles in one and two dimensions. The last chapter addresses the dynamical mean field theory (DMFT). The book is based on the author's long years of experience as a lecturer and researcher. It also includes reviews of recent focus topics in condensed matter physics, enabling readers to not only grasp conventional condensed matter theories but also to catch up on the latest developments in the field |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed February 21, 2020) |
| Subject |
Many-body problem.
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Quantum theory.
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Quantum Theory
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Many-body problem
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Quantum theory
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| Form |
Electronic book
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| ISBN |
9784431553939 |
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4431553932 |
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