50 Years of Anderson Localization

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World Scientific, 2010 - Science - 597 pages
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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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Contents

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
General Formalism and Applications P W ole and D Vollhardt
43
Chapter 5 Anderson Localization and Supersymmetry K B Efetov
73
Criticality Symmetries and Topologies A D Mirlin F Evers I V Gornyi and 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 B uttiker and M Moskalets
169
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 and K Slevin
347
Established Facts and Open Questions S V Kravchenko and M P Sarachik
361
Chapter 18 Disordered Electron Liquid with Interactions A M Finkelstein
385
Chapter 19 TypicalMedium Theory of MottAnderson Localization V Dobrosavljevi c
425
Chapter 20 Anderson Localization vs MottHubbard MetalInsulator Transition in Disordered Interacting Lattice Fermion Systems K Byczuk W Hofste...
473

Electric and Thermal Transport Y Imry and A Amir
191
Chapter 10 Localization and the MetalInsulator 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 ElectronElectron Interaction Effects in thin Metal Wires and Films N Giordano
269
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 and J Wang
559
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