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50 Years Of Anderson Localization

Author: Elihu Abrahams
Publisher: World Scientific
ISBN: 9814299073
Size: 49.74 MB
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This unique volume celebrates the five decades of the impact of Anderson localization on modern physics. In addition to the historical perspective on its origin, it provides a comprehensive description of the experimental and theoretical aspects of Anderson localization.

Anderson Localization And Its Ramifications

Author: Tobias Brandes
Publisher: Springer Science & Business Media
ISBN: 9783540407850
Size: 21.19 MB
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The phenomenon of localization of the electronic wave function in a random medium can be regarded as the key manifestation of quantum coherence in a condensed matter system. As one of the most remarkable phenomena in condensed matter physics discovered in the 20th century, the localization problem is an indispensable part of the theory of the quantum Hall effects and rivals superconductivity in its significance as a manifestation of quantum coherence at a macroscopic scale. The present volume, written by some of the leading experts in the field, is intended to highlight some of the recent progress in the field of localization, with particular emphasis on the effect of interactions on quantum coherence. The chapters are written in textbook style and should serve as a reliable and thorough introduction for advanced students or researchers already working in the field of mesoscopic physics.

Anderson Localization

Author: Y. Nagaoka
Publisher: Springer Science & Business Media
ISBN: 3642818412
Size: 39.83 MB
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This volume contains the proceedings of the Fourth Taniguchi International Symposium on the Theory of Condensed Matter, which was held at Senkari Semi nar House of Kwansei Gakuin Universi~y in Sanda-shi, Japan, during the period of 3-8 November 1981. The topic of the symposium was "Anderson rocalization," one of the most fundamental problems in condensed-matter physics. Since Anderson's classic paper was published in 1958, much theoretical and experimental effort has been performed to study the problem of electron localization in a random potential. Quite recently, Abrahams, Anderson, Licciardello, and Ramakrishnan proposed a scaling theory of the Anderson lo calization which made it possible to perform microscopic investigations. Rapid progress has followed and we are now getting a coherent picture of the behavior of electrons in disordered systems. When we organized the symposium, we asked Dr. Anderson to participate in it and to give a review talk on theoretical aspects of the problem. Though he kindly accepted our invitation, he could not come due to a sudden illness. A review talk was given by Professor Thouless who kindly accepted our request to take the place of Dr. Anderson. Fortunately, Dr. Anderson has since re covered from his illness.

Multi Scale Analysis For Random Quantum Systems With Interaction

Author: Victor Chulaevsky
Publisher: Springer Science & Business Media
ISBN: 1461482267
Size: 58.64 MB
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The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

Optical Properties Of Photonic Structures

Author: Mikhail F. Limonov
Publisher: Taylor & Francis
ISBN: 1439871922
Size: 28.77 MB
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The collection of articles in this book offers a penetrating shaft into the still burgeoning subject of light propagation and localization in photonic crystals and disordered media. While the subject has its origins in physics, it has broad significance and applicability in disciplines such as engineering, chemistry, mathematics, and medicine. Unlike other branches of physics, where the phenomena under consideration require extreme conditions of temperature, pressure, energy, or isolation from competing effects, the phenomena related to light localization survive under the most ordinary of conditions. This provides the science described in this book with broad applicability and vitality. However, the greatest challenge to the further development of this field is in the reliable and inexpensive synthesis of materials of the required composition, architecture and length scale, where the proper balance between order and disorder is realized. Similar challenges have been faced and overcome in fields such as semiconductor science and technology. The challenge of photonic crystal synthesis has inspired a variety of novel fabrication protocols such as self-assembly and optical interference lithography that offer much less expensive approaches than conventional semiconductor microlithography. Once these challenges are fully met, it is likely that light propagation and localization in photonic microstructures will be at the heart of a 21st-century revolution in science and technology. —From the Introduction, Sajeev John, University of Toronto, Ontario, Canada One of the first books specifically focused on disorder in photonic structures, Optical Properties of Photonic Structures: Interplay of Order and Disorder explores how both order and disorder provide the key to the different regimes of light transport and to the systematic localization and trapping of light. Collecting contributions from leaders of research activity in the field, the book covers many important directions, methods, and approaches. It describes various one-, two-, and three-dimensional structures, including opals, aperiodic Fibonacci-type photonic structures, photonic amorphous structures, photonic glasses, Lévy glasses, and hypersonic, magnetophotonic, and plasmonic–photonic crystals with nanocavities, quantum dots, and lasing action. The book also addresses practical applications in areas such as optical communications, optical computing, laser surgery, and energy.

Mathematical Physics Of Quantum Wires And Devices

Author: N.E. Hurt
Publisher: Springer Science & Business Media
ISBN: 9780792362883
Size: 44.52 MB
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This is the first book to present a comprehensive treatment of the mathematical physics of quantum wires and devices. The focus is on the recent results in the area of the spectral theory of bent and deformed quantum wires, simple quantum devices, Anderson localization, the quantum Hall effect and graphical models for quantum wire systems. The Selberg trace formula for finite volume graphical models is reviewed. Examples and relationships to recent work on acoustic and fluid flow, trapped states and spectral resonances, quantum chaos, random matrix theory, spectral statistics, point interactions, photonic crystals, Landau models, quantum transistors, edge states and metal-insulator transitions are developed. Problems related to modeling open quantum devices are discussed. The research of Exner and co-workers in quantum wires, Stollmann, Figotin, Bellissard et al. in the area of Anderson localization and the quantum Hall effect, and Bird, Ferry, Berggren and others in the area of quantum devices and their modeling is surveyed. The work on finite volume graphical models is interconnected to recent work on Ramanujan graphs and diagrams, the Phillips-Sarnak conjectures, L-functions and scattering theory. Audience: This book will be of use to physicists, mathematicians and engineers interested in quantum wires, quantum devices and related mesoscopic systems.

Ill Condensed Matter

Author: R Balian
Publisher: World Scientific
ISBN: 9814531898
Size: 36.81 MB
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Contents: Percolation and Localization (D J Thouless)Disordered Systems — Experimental Viewpoint (J Joffrin)Lectures on Amorphous Systems (P W Anderson)Elementary Algebraic Topology Related to the Theory of Defects and Textures (V Poenaru)Models of Disordered Materials (S Kirkpatrick)Thermal and Geometrical Critical Phenomena in Random Systems (T C Lukensky)A Short Guide to Polymer Physics (P-G de Gennes)and 9 seminars Readership: Graduate students and researchers in condensed matter physics.

More Is Different

Author: N. Phuan Ong
Publisher: Princeton University Press
ISBN: 9780691088662
Size: 28.84 MB
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This book presents articles written by leading experts surveying several major subfields in Condensed Matter Physics and related sciences. The articles are based on invited talks presented at a recent conference honoring Nobel laureate Philip W. Anderson of Princeton University, who coined the phrase "More is different" while formulating his contention that all fields of physics, indeed all of science, involve equally fundamental insights. The articles introduce and survey current research in areas that have been close to Anderson's interests. Together, they illustrate both the deep impact that Anderson has had in this multifaceted field during the past half century and the progress spawned by his insights. The contributors cover numerous topics under the umbrellas of superconductivity, superfluidity, magnetism, electron localization, strongly interacting electronic systems, heavy fermions, and disorder and frustration in glass and spin-glass systems. They also describe interdisciplinary areas such as the science of olfaction and color vision, the screening of macroions in electrolytes, scaling and renormalization in cosmology, forest fires and the spread of measles, and the investigation of "NP-complete" problems in computer science. The articles are authored by Philip W. Anderson, Per Bak and Kan Chen, G. Baskaran, Juan Carlos Campuzano, Paul Chaikin, John Hopfield, Bernhard Keimer, Scott Kirkpatrick and Bart Selman, Gabriel Kotliar, Patrick Lee, Yoshiteru Maeno, Marc Mezard, Douglas Osheroff et al., H. R. Ott, L. Pietronero et al., T. V. Ramakrishnan, A. Ramirez, Myriam Sarachik, T. Senthil and Matthew P. A. Fisher, B. I. Shklovskii et al., and F. Steglich et al.

Random Operators

Author: Michael Aizenman
Publisher: American Mathematical Soc.
ISBN: 1470419130
Size: 60.69 MB
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This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Bcs 50 Years

Author: Dimitri Feldman
Publisher: World Scientific
ISBN: 9814360864
Size: 62.60 MB
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Named a Top Five Book of 2011 by "Physics Today," USA. The BCS theory of superconductivity developed in 1957 by Bardeen, Cooper and Schrieffer has been remarkably successful in explaining the properties of superconductors. In addition, concepts from BCS have been incorporated into diverse fields of physics, from nuclear physics and dense quark matter to the current standard model. Practical applications include SQUIDs, magnetic resonance imaging, superconducting electronics and the transmission of electricity. This invaluable book is a compilation of both a historical account and a discussion of the current state of theory and experiment. With contributions from many prominent scientists, it aims to introduce students and researchers to the origins, the impact and the current state of the BCS theory. Contents: "Historical Perspectives: "Remembrance of Superconductivity Past "(L N Cooper)"The Road to BCS "(J R Schrieffer)"Development of Concepts in Superconductivity "(J Bardeen)"Failed Theories of Superconductivity "(J Schmalian)"Nuclear Magnetic Resonance and the BCS Theory "(C P Slichter)"Superconductivity: From Electron Interaction to Nuclear Supefluidity "(D Pines)"Developing BCS Ideas in the Former Soviet Union "(L P Gor'kov)"BCS: The Scientific ?Love of My Life? "(P W Anderson)""Fluctuations, Tunneling and Disorder: "SQUIDs: Then and Now "(J Clarke)"Resistance in Superconductors "(B I Halperin et al.)"Cooper Pair Breaking "(P Fulde)"Superconductor-Insulator Transitions "(A M Goldman)"Novel Phases of Vortices in Superconductors "(P Le Doussal)"Breaking Translational Invariance by Population Imbalance: The Fulde?Ferrell?Larkin?Ovchinnikov States "(G Zwicknagl & J Wosnitza)""New Superconductors: "Predicting and Explaining "Tc" and Other Properties of BCS Superconductors "(M L Cohen)"The Evolution of HTS: "Tc"-Experiment Perspectives "(C W Chu)"The Evolution of High-Temperature Superconductivity: Theory Perspective "(E Abrahams)""BCS Beyond Superconductivity: "The Superfluid Phases of Liquid 3He: BCS Theory "(A J Leggett)"Superfluidity in a Gas of Strongly Interacting Fermions "(W Ketterle et al.)"BCS from Nuclei and Neutron Stars to Quark Matter and Cold Atoms "(G Baym)"Energy Gap, Mass Gap, and Spontaneous Symmetry Breaking "(Y Nambu)"BCS as Foundation and Inspiration: The Transmutation of Symmetry "(F Wilczek)"From BCS to the LHC "(S Weinberg)" Readership: Students, researchers and academics interested in BCS theory and its origin.