50 Years of Anderson Localization.
Title:
50 Years of Anderson Localization.
Author:
Abrahams, Elihu.
ISBN:
9789814299084
Personal Author:
Physical Description:
1 online resource (610 pages)
Contents:
CONTENTS -- Preface -- INTRODUCTION -- References -- Chapter 1 Thoughts on Localization P. W. Anderson -- References -- Chapter 2 Anderson Localization in the Seventies and Beyond D. Thouless -- 1. Introduction -- 2. Characteristics of Localized States -- 3. Scaling Properties -- 4. Effects of Interactions -- 5. Quantum Hall Effect -- 6. Localization in Other Systems -- 7. Summary -- Acknowledgments -- References -- Chapter 3 Intrinsic Electron Localization in Manganites T. V. Ramakrishnan -- 1. Introduction -- 2. A Two Fluid Model for Manganites -- 3. Localization in the Manganites -- 4. Comparison with Experiments -- Acknowledgments -- References -- Chapter 4 Self-Consistent Theory of Anderson Localization: General Formalism and Applications P. W ole and D. Vollhardt -- 1. Introduction to Anderson Localization -- 1.1. Brief historical review -- 1.2. Electrons and classical waves in disordered systems -- 1.3. Weak localization -- 1.4. Strong localization and the Anderson transition -- 2. Fundamental Theoretical Concepts of Anderson Localization -- 2.1. Scaling theory of the conductance -- 2.2. Renormalization group equation -- 2.3. Critical exponents -- 2.4. Dynamical scaling -- 3. Renormalized Perturbation Theory of Quantum Transport in Disordered Media -- 4. Self-Consistent Theory of Anderson Localization -- 4.1. Results of the self-consistent theory of Anderson localization -- 5. Applications of the Self-Consistent Theory of Anderson Localization -- 5.1. Effect of static magnetic and electric fields -- 5.1.1. Magnetic fields -- 5.1.2. Electric fields -- 5.2. Anisotropic systems, films and wires -- 5.3. Anderson localization of classical waves -- 5.4. Transport through open interfaces -- 6. Conclusion -- Acknowledgments -- References -- Chapter 5 Anderson Localization and Supersymmetry K. B. Efetov -- 1. Introduction.
2. Supermatrix Non-Linear -Model -- 3. Level Statistics in Small Metal Particles -- 4. Anderson Localization in Quantum Wires -- 5. Anderson Localization in 2 and 2 + Dimensions -- 6. Anderson Metal{Insulator Transition on the Bethe Lattice or in a High Dimensionality -- 7. Discussion -- Acknowledgments -- References -- Chapter 6 Anderson Transitions: Criticality, Symmetries and Topologies A. D. Mirlin, F. Evers, I. V. Gornyi and P. M. Ostrovsky -- 1. Introduction -- 2. Anderson Transitions in Conventional Symmetry Classes -- 2.1. Scaling theory, observables and critical behavior -- 2.2. Field-theoretical description -- 2.2.1. Effective field theory: Non-linear -model -- 2.2.2. RG in 2 + dimensions -- -expansion -- 2.3. Critical wave functions: Multifractality -- 2.3.1. Scaling of inverse participation ratios and correlations at criticality -- 2.3.2. Singularity spectrum f( ) -- 2.3.3. Symmetry of the multifractal spectra -- 2.3.4. Dimensionality dependence of multifractality -- 2.3.5. Surface vs. bulk multifractality -- 2.4. Additional comments -- 2.5. Anderson transition in d = : Bethe lattice -- 3. Symmetries of Disordered Systems -- 3.1. Wigner-Dyson classes -- 3.2. Relation to symmetric spaces -- 3.3. Chiral classes -- 3.4. Bogoliubov-de Gennes classes -- 3.5. Perturbative RG for -models of different symmetry classes -- 4. Criticality in 2D -- 4.1. Mechanisms of criticality in 2D -- 4.1.1. Broken spin-rotation invariance: Metallic phase -- 4.1.2. Chiral classes: Vanishing -function -- 4.1.3. Broken time-reversal invariance: Topological -term and quantum Hall criticality -- 4.1.4. Z2 topological term -- 4.1.5. Wess-Zumino term -- 4.2. Disordered Dirac Hamiltonians and graphene -- 4.2.1. Symmetries of disorder and types of criticality -- 4.2.2. Decoupled nodes: Disordered single-avor Dirac fermions and quantum-Hall-type criticality.
4.2.3. Preserved C0 chirality: Random gauge fields -- 4.2.4. Disorders preserving Cz chirality: Gade-Wegner criticality -- 5. Electron-Electron Interaction Effects -- 6. Topological Insulators -- 6.1. Symmetry classification of topological insulators -- 6.2. Z2 topological insulators in 2D and 3D systems of class AII -- 6.3. Interaction effects on Z2 topological insulators of class AII -- 7. Summary -- References -- Chapter 7 Scaling of von Neumann Entropy at the Anderson Transition S. Chakravarty -- 1. Introduction -- 2. Statistical Field Theory of Localization -- 3. von Neumann Entropy -- 4. von Neumann Entropy in Disordered Noninteracting Electronic Systems -- 5. von Neumann Entropy in the Three-Dimensional Anderson Model -- 6. von Neumann Entropy in the Integer Quantum Hall System -- 7. A Brief Note on the Single-Site von Neumann Entropy -- 8. Epilogue -- Acknowledgments -- References -- Chapter 8 From Anderson Localization to Mesoscopic Physics M. B uttiker and M. Moskalets -- 1. Introduction -- 2. Charge Transfer from the Scattering Matrix -- 3. The Wigner{Smith Delay Time and Energy Shift Matrix -- 4. The Internal Response -- 4.1. Quantum pumping -- 4.2. Pumping in insulators and metals -- 4.3. Scattering formulation of ac response -- 4.4. Capacitance, emittances, partial density of states -- 4.5. Ac response of a localized state -- 5. Nonlinear AC Response of a Localized State -- 6. Quantized Charge Emission from a Localized State -- 6.1. Multi-particle emission from multiple localized states -- 7. Conclusion -- Acknowledgments -- References -- Chapter 9 The Localization Transition at Finite Temperatures: Electric and Thermal Transport Y. Imry and A. Amir -- 1. Introduction -- 2. The Zero and Finite Temperature Macroscopic Conductivity Around the Anderson Localization Transition -- 2.1. The Thouless picture within the tunnel-junction model.
2.2. The critical behavior of the T = 0 conductivity -- 2.3. The conductivity at nite temperatures -- 2.4. Analysis of (T -- - Em) -- 3. Thermal and Thermoelectric Transport -- 3.1. General relationships -- 3.2. Onsager relations in a magnetic field -- 3.3. Analysis of the thermopower -- 4. Brief Discussion of Experiments -- 5. Concluding Remarks -- Appendix - The Heat Carried by a Transport Quasiparticle -- Acknowledgments -- References -- Chapter 10 Localization and the Metal-Insulator Transition - Experimental Observations R. C. Dynes -- 1. Introduction -- 2. Two Dimensions -- 3. Three Dimensions -- 4. Summary -- Acknowledgments -- References -- Chapter 11 Weak Localization and its Applications as an Experimental Tool G. Bergmann -- 1. Introduction -- 2. The Physics of Weak Localization -- 2.1. The echo of a scattered electron wave -- 2.2. Time of flight experiment in a magnetic field -- 3. Spin-Orbit and Inelastic Scattering -- 3.1. The inelastic dephasing -- 4. Magnetic Scattering -- 4.1. Magnetism of 3d, 4d and 5d surface impurities -- 4.1.1. 3d surface impurities Ti, V, Cr, Mn, Fe, Co, Ni -- 4.1.2. 4d surface impurities Nb, Mo, Ru, Rh, Pd -- 4.1.3. 5d surface impurities W and Re -- 4.2. Kondo impurities -- 4.2.1. Interacting Kondo impurities -- 5. Tunneling Effect -- 5.1. Proximity effect -- 6. Conclusion -- References -- Chapter 12 Weak Localization and Electron-Electron Interaction Effects in thin Metal Wires and Films N. Giordano -- 1. Introduction -- 2. Resistance of Thin Wires: Dependence on Temperature, Diameter, and Length -- 3. Early Observation of Mesoscopic Effects -- 4. Magnetoresistance and Electron Phase Coherence -- 5. Universal Conductance Fluctuations -- 6. Mesoscopic Photovoltaic Effect -- 7. Behavior of Parallel Metal Layers: Some Puzzles -- 8. Conclusions -- Acknowledgments -- References.
Chapter 13 Inhomogeneous Fixed Point Ensembles Revisited F. J. Wegner -- 1. Introduction -- 2. One-Dimensional Chains -- 2.1. Thouless relation -- 2.2. Ziman's model -- 2.3. Further one-dimensional results -- 3. Bosons From One To Two Dimensions -- 3.1. One-dimensional chain -- 3.2. Bosonic excitations discussed by Gurarie and Chalker -- 4. Electronic Systems In Two Dimensions -- 4.1. Conductivity in two dimensions -- 4.2. Chiral and Bogolubov-de Gennes models in d = 2 dimensions -- 4.3. Power law for density of states, finite localization length -- 5. Conclusion -- Acknowledgments -- References -- Chapter 14 Quantum Network Models and Classical Localization Problems J. Cardy -- 1. Introduction -- 2. General Network Models -- 3. The Main Theorems -- 4. Two-Dimensional Models -- 4.1. The L-lattice -- 4.2. The Manhattan Lattice -- 4.3. Other 2d lattices -- 5. Three-Dimensional Models -- 5.1. Diamond lattice -- 5.2. 3d L-lattice and Manhattan lattice -- 6. Summary and Further Remarks -- Acknowledgments -- References -- Chapter 15 Mathematical Aspects of Anderson Localization T. Spencer -- 1. Introduction -- 2. One Dimension: History, Results and Conjectures -- 3. Finite Volume Criteria for Localization on Zd -- 4. The Nonlinear Schr odinger Equation with a Random Potential -- 5. A Simple SUSY Model of the Anderson Transition in 3D -- 6. Role of Ward Identities in the Proof -- 7. Edge Reinforced Random Walk and Localization -- Acknowledgments -- References -- Chapter 16 Finite Size Scaling Analysis of the Anderson Transition B. Kramer, A. MacKinnon, T. Ohtsuki and K. Slevin -- 1. Introduction -- 2. The Anderson Model of Disordered Systems -- 3. Finite Size Scaling Analysis of the Anderson Transition -- 3.1. Finite size scaling -- 3.2. Quasi-one dimensional localization length -- 3.3. The transfer matrix method -- 3.4. The correlation length.
4. The Critical Exponents.
Abstract:
In his groundbreaking paper Absence of diffusion in certain random lattices (1958), Philip W. Anderson originated, described and developed the physical principles underlying the phenomenon of the localization of quantum objects due to disorder. Anderson's 1977 Nobel Prize citation featured that paper, which was fundamental for many subsequent developments in condensed matter theory and technical applications. After more than a half century, the subject continues to be of fundamental importance. In particular, in the last 25 years, the phenomenon of localization has proved to be crucial for the understanding of the Quantum Hall Effect, mesoscopic fluctuations in small conductors, some aspects of quantum chaotic behavior, and most recently the localization and collective modes of electromagnetic and matter waves. This unique and invaluable volume celebrates the five decades of the impact of Anderson Localization on modern physics.In addition to the historical perspective on its origin, the volume provides a comprehensive description of the experimental and theoretical aspects of Anderson localization, together with its application in various areas, which include disordered metals and the metal-insulator transition, mesoscopic physics, classical systems and light, strongly-correlated systems, and mathematical models. The volume is edited by E Abrahams, who, as a major contributor in the field of localization, has published several papers on the celebrated scaling theory of localization. A distinguished group of experts, each of whom has left his mark on the developments of this fascinating theory, contribute their personal insights in this volume.They are: P W Anderson (Nobel Laureate, 1977), G Bergmann (University of Southern California), M Buttiker (University of Geneva), J Cardy (Oxford University), S Chakravarty (University of California, Los
Angeles), V Dobrosavljevic (Florida State University), R C Dynes (University of California, San Diego), K B Efetov (Ruhr University Bochum), A M Finkel'stein (Texas A&M University), A Genack (Queens College, New York), N Giordano (Purdue University), Y Imry (Weizmann Institute), B Kramer(University of Hamburg), S V Kravchenko (Northeastern University), A Mirlin(University of Karlsruhe), A M M Pruisken (University of Amsterdam), T V Ramakrishnan (Indian Institute of Science), T Spencer (Institute of Advanced Study, Princeton), D J Thouless (University of Washington), D Vollhardt (University of Augsburg) and F J Wegner (University of Heidelberg).
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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