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50 Years of Anderson Localization

50 Years of Anderson Localization Author Elihu Abrahams
ISBN-10 9789814299077
Release 2010
Pages 597
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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.

Optical Properties of Photonic Structures

Optical Properties of Photonic Structures Author Mikhail F. Limonov
ISBN-10 9781439871928
Release 2016-04-19
Pages 566
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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.

Ill Condensed Matter

Ill Condensed Matter Author R Balian
ISBN-10 9789814531894
Release 1984-03-01
Pages 636
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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.

PWA90 A Lifetime of Emergence

PWA90  A Lifetime of Emergence Author Premi Chandra
ISBN-10 9789814733649
Release 2015-12-21
Pages 252
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' In a remarkable career spanning more than six decades, Philip W Anderson has made many fundamental contributions to physics. As codified in his oft-quoted phrase "More is Different", Anderson has been the most forceful and persuasive proponent of the radical, but now ubiquitous, viewpoint of emergent phenomena: truly fundamental concepts that can and do emerge from studies of Nature at each layer of complexity or energy scale. Anderson''s ideas have also extended deeply into other areas of physics, including the Anderson–Higgs mechanism and the dynamics of pulsars. PWA90: A Lifetime of Emergence is a volume of original scientific essays and personal reminiscences of Philip W Anderson by experts in the field, that were presented as part of "PWA90: Emergent Frontiers of Condensed Matter" meeting held at Princeton in December 2013 to highlight Anderson''s contributions to physics. Contents: Recollections of a Graduate Student (Khandker A Muttalib)P W Anderson Seen Through the Eyes of a Student (Clare C Yu)Random Walks in Anderson''s Garden: A Journey from Cuprates to Cooper Pair Insulators and Beyond (G Baskaran)Some Reminiscences on Anderson Localization (Elihu Abrahams)Anderson and Condensed Matter Physics (T V Ramakrishnan)Superfluidity and Symmetry Breaking — An Anderson Living Legacy (Frank Wilczek)Phil Anderson and Gauge Symmetry Breaking (Edward Witten)A Short History of the Theory and Experimental Discovery of Superfluidity in 3He (W F Brinkman)Superconductivity in a Terrestrial Liquid: What Would It Be Like? (A J Leggett)40 Years of Quantum Spin Liquid: A Tale of Emergence from Frustration (Patrick A Lee)High Tc Superconductivity and RVB (Mohit Randeria)Paired Insulators and High Temperature Superconductors (T H Geballe and S A Kivelson)Special Properties of High Tc Cuprates, Radically Different from Other Transition Metal Oxides (T M Rice)From Bacteria to Artificial Cells, the Problem of Self-Reproduction (Albert Libchaber)Spin Glasses and Frustration (Scott Kirkpatrick)Frustration and Fluctuations in Systems with Quenched Disorder (D L Stein)Phil Anderson''s Magnetic Ideas in Science (Piers Coleman) Readership: Students, academics and researchers in condensed matter. Keywords:P W Anderson;Superfluidity;Anderson–Higgs Mechanism;Pulsars;Condensed Matter Physics;Anderson;Localization;High-Temperature Superconductors;Spin Classes'

Multi scale Analysis for Random Quantum Systems with Interaction

Multi scale Analysis for Random Quantum Systems with Interaction Author Victor Chulaevsky
ISBN-10 9781461482260
Release 2013-09-20
Pages 238
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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.

Anderson Localization and Its Ramifications

Anderson Localization and Its Ramifications Author Tobias Brandes
ISBN-10 3540407855
Release 2003-09-11
Pages 315
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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.

Advanced Solid State Physics

Advanced Solid State Physics Author Philip Phillips
ISBN-10 9780521194907
Release 2012-03-01
Pages 402
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Introduces students to the key research topics within modern solid state physics with the minimum of mathematics.

Random Operators

Random Operators Author Michael Aizenman
ISBN-10 9781470419134
Release 2015-12-11
Pages 326
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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.

More is Different

More is Different Author N. Phuan Ong
ISBN-10 0691088667
Release 2001
Pages 345
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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.

Introduction to Quantum Graphs

Introduction to Quantum Graphs Author Gregory Berkolaiko
ISBN-10 9780821892114
Release 2013
Pages 270
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A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Fluctuations and Localization in Mesoscopic Electron Systems

Fluctuations and Localization in Mesoscopic Electron Systems Author Martin Janssen
ISBN-10 9812798927
Release 2001
Pages 205
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The quantum phenomena of tunneling and interference show up not only in the microscopic world of atoms and molecules, but also in cold materials of the real world, such as metals and semiconductors. Though not fully macroscopic, such mesoscopic systems contain a huge number of particles, and the holistic nature of quantum mechanics becomes evident already in simple electronic measurements. The measured quantity fluctuates as a function of applied fields in an unpredictable, yet reproducible way. Despite this fingerprint character of fluctuations, their statistical properties are universal, i.e. they are the same for a large class of different mesoscopic systems, having only very few parameters in common. Localization of electrons is a dramatic effect of destructive interference. As a consequence a metal can become an insulator while reaching mesoscopic scales. Based on elementary quantum and statistical physics, this text introduces the theory of mesoscopic electron systems. It focuses on universal characteristics of fluctuations and on the localization mechanism. General concepts and methods are stressed, such as scaling laws for distribution functions. Tools from condensed matter theory are used flexibly. Involved technical details are skipped so as to present a broad overview of the field, including topics like quantum dots, the quantum Hall effect and a number of the most recent developments. Contents: Experimental Facts; Basic Theoretical Models and Tools; Idealized Systems; Towards Realistic Systems; The Localization-Delocalization Transition. Readership: Condensed matter and theoretical physicists.

Spectral Theory and Mathematical Physics

Spectral Theory and Mathematical Physics Author Marius Mantoiu
ISBN-10 9783319299921
Release 2016-06-30
Pages 255
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The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

Conductor Insulator Quantum Phase Transitions

Conductor Insulator Quantum Phase Transitions Author Vladimir Dobrosavljevic
ISBN-10 9780199592593
Release 2012-06-01
Pages 566
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When many particles come together how do they organize themselves? And what destroys this organization? Combining experiments and theory, this book describes intriguing quantum phases - metals, superconductors and insulators - and transitions between them. It captures the excitement and the controversies on topics at the forefront of research.

Radiation Effects in Solids

Radiation Effects in Solids Author Kurt E. Sickafus
ISBN-10 9781402052958
Release 2007-05-22
Pages 592
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This is a comprehensive overview of fundamental principles and relevant technical issues associated with the behavior of solids exposed to high-energy radiation. These issues are important to the development of materials for existing fission reactors or future fusion and advanced reactors for energy production; to the development of electronic devices such as high-energy detectors; and to the development of novel materials for electronic and photonic applications.

Scattering and Localization of Classical Waves in Random Media

Scattering and Localization of Classical Waves in Random Media Author Ping Sheng
ISBN-10 9971505398
Release 1990
Pages 635
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The past decade has witnessed breakthroughs in the understanding of the wave localization phenomena and its implications for wave multiple scattering in inhomogeneous media. This book brings together review articles written by noted researchers in this field in a tutorial manner so as to give the readers a coherent picture of its status. It would be valuable both as an up-to-date reference for active researchers as well as a readable source for students looking to gain an understanding of the latest results.

Transport Processes in Macroscopically Disordered Media

Transport Processes in Macroscopically Disordered Media Author Andrei A. Snarskii
ISBN-10 1441982922
Release 2016-01-06
Pages 310
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Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to Percolation reflects on recent advances in the understanding of percolation systems to present a wide range of transport phenomena in inhomogeneous disordered systems. Further developments in the theory of macroscopically inhomogeneous media are also addressed. These developments include galvano-electric, thermoelectric, elastic properties, 1/f noise and higher current momenta, Anderson localization, and harmonic generation in composites in the vicinity of the percolation threshold. The book describes how one can find effective characteristics, such as conductivity, dielectric permittivity, magnetic permeability, with knowledge of the distribution of different components constituting an inhomogeneous medium. Considered are a wide range of recent studies dedicated to the elucidation of physical properties of macroscopically disordered systems. This book contains a straightforward set of useful tools which will allow the reader to derive the basic physical properties of complicated systems together with their corresponding qualitative characteristics and functional dependencies.

Nanoscale Phase Separation and Colossal Magnetoresistance

Nanoscale Phase Separation and Colossal Magnetoresistance Author Elbio Dagotto
ISBN-10 9783662052440
Release 2013-03-14
Pages 459
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The study of the spontaneous formation of nanostructures in single crystals of several compounds is now a major area of research in strongly correlated electrons. These structures appear to originate in the competition of phases. The book addresses nanoscale phase separation, focusing on the manganese oxides known as manganites that have the colossal magnetoresistance (CMR) effect of potential relevance for device applications. It is argued that the nanostructures are at the heart of the CMR phenomenon. The book contains updated information on manganite research directed to experts, both theorists and experimentalists. However, graduate students or postdocs will find considerable introductory material, including elements of computational physics.