50 years of anderson localization

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50 Years Of Anderson Localization

Author : Elihu Abrahams
ISBN : 9789814299077
Genre : Science
File Size : 86. 15 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.

Multi Scale Analysis For Random Quantum Systems With Interaction

Author : Victor Chulaevsky
ISBN : 9781461482260
Genre : Mathematics
File Size : 51. 19 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.

Journal Of The Physical Society Of Japan

Author :
ISBN : CHI:82282339
Genre : Physics
File Size : 31. 86 MB
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Introduction To Quantum Graphs

Author : Gregory Berkolaiko
ISBN : 9780821892114
Genre : Mathematics
File Size : 73. 6 MB
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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.

Cnrs International Magazine

Author :
ISBN : STANFORD:36105132728374
Genre : Research
File Size : 26. 45 MB
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Pwa90 A Lifetime Of Emergence

Author : Premi Chandra
ISBN : 9789814733649
Genre : Science
File Size : 39. 77 MB
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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'

Graphene

Author : Mikhail I. Katsnelson
ISBN : 9780521195409
Genre : Science
File Size : 49. 99 MB
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An important introduction to graphene, its physics and potentially significant applications, for graduate students, physicists and materials science researchers.

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