50 Years Of Anderson Localization

by Elihu Abrahams

Overview

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 physics 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 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 has been a contributor in the field 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: A Amir (Weizmann Institute of Science), P W Anderson (Princeton University), G Bergmann (University of Southern California), M Büttiker (University of Geneva), K Byczuk (University of Warsaw & University of Augsburg), J Cardy (University of Oxford), S Chakravarty (University of California, Los Angeles), V Dobrosavljević (Florida State University), R C Dynes (University of California, San Diego), K B Efetov (Ruhr University Bochum), F Evers (Karlsruhe Institute of Technology), A M Finkel'stein (Weizmann Institute of Science & Texas A&M University), A Genack (Queens College, CUNY), N Giordano (Purdue University), I V Gornyi (Karlsruhe Institute of Technology), W Hofstetter (Goethe University Frankfurt), Y Imry (Weizmann Institute of Science), B Kramer (Jacobs University Bremen), S V Kravchenko (Northeastern University), A MacKinnon (Imperial College London), A D Mirlin (Karlsruhe Institute of Technology), M Moskalets (NTU “Kharkiv Polytechnic Institute”), T Ohtsuki (Sophia University), P M Ostrovsky (Karlsruhe Institute of Technology), A M M Pruisken (University of Amsterdam), T V Ramakrishnan (Indian Institute of Science), M P Sarachik (City College, CUNY), K Slevin (Osaka University), T Spencer (Institute for Advanced Study, Princeton), D J Thouless (University of Washington), D Vollhardt (University of Augsburg), J Wang (Queens College, CUNY), F J Wegner (Ruprecht-Karls-University) and P Wölfle (Karlsruhe Institute of Technology).

Product Details

ISBN-13:	9789814299077
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	06/28/2010
Pages:	612
Product dimensions:	6.50(w) x 9.70(h) x 1.10(d)

Table of Contents

Preface v

Chapter 1 Thoughts on Localization P. W. Anderson 1

Chapter 2 Anderson Localization in the Seventies and Beyond D. Thouless 7

Chapter 3 Intrinsic Electron Localization in Manganites T. V. Ramakrishnan 27

Chapter 4 Self-Consistent Theory of Anderson Localization: General Formalism and Applications P. Wölfle D. Vollhardt 43

Chapter 5 Anderson Localization and Supersymmetry K. B. Efetov 73

Chapter 6 Anderson Transitions: Criticality, Symmetries and Topologies A. D. Mirlin F. Evers I. V. Gornyi P. M. Ostrovsky 107

Chapter 7 Scaling of von Neumann Entropy at the Anderson Transition S. Chakravarty 151

Chapter 8 From Anderson Localization to Mesoscopic Physics M. Büttiker M. Moskalets 169

Chapter 9 The Localization Transition at Finite Temperatures: Electric and Thermal Transport Y. Imry A. Amir 191

Chapter 10 Localization and the Metal-Insulator Transition-Experimental Observations R. C. Dynes 213

Chapter 11 Weak Localization and its Applications as an Experimental Tool G. Bergmann 231

Chapter 12 Weak Localization and Electron-Electron Interaction Effects in thin Metal Wires and Films N. Giordano 269

Chapter 13 Inhomogeneous Fixed Point Ensembles Revisited F. J. Wegner 289

Chapter 14 Quantum Network Models and Classical Localization Problems J. Cardy 301

Chapter 15 Mathematical Aspects of Anderson Localization T. Spencer 327

Chapter 16 Finite Size Scaling Analysis of the Anderson Transition B. Kramer A. MacKinnon T. Ohtsuki K. Slevin 347

Chapter 17 A Metal-Insulator Transition in 2D: Established Facts and Open Questions S. V. Kravchenko M. P. Sarachik 361

Chapter 18 Disordered Electron Liquid with Interactions A. M. Finkel'stein 385

Chapter 19 Typical-Medium Theory of Mott-Anderson Localization V. Dobrosavljevic 425

Chapter 20 Anderson Localization vs. Mott-Hubbard Metal-Insulator Transition in Disordered, Interacting Lattice Fermion Systems K. Byczuk W. Hofstetter D. Vollhardt 473

Chapter 21 Topological Principles in the Theory of Anderson Localization A. M. M. Pruisken 503

Chapter 22 Speckle Statistics in the Photon Localization Transition A. Z. Genack J. Wang 559