50 years of anderson localization

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50 Years Of Anderson Localization

Author : Elihu Abrahams
ISBN : 9789814299077
Genre : Science
File Size : 57. 30 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. 72 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.

Introduction To Quantum Graphs

Author : Gregory Berkolaiko
ISBN : 9780821892114
Genre : Mathematics
File Size : 67. 90 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.

Journal Of The Physical Society Of Japan

Author :
ISBN : CHI:82282339
Genre : Physics
File Size : 30. 94 MB
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Graphene

Author : Mikhail I. Katsnelson
ISBN : 9780521195409
Genre : Science
File Size : 36. 55 MB
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An important introduction to graphene, its physics and potentially significant applications, for graduate students, physicists and materials science researchers.

Lessons From Nanoelectronics

Author : Supriyo Datta
ISBN : 9814335290
Genre : Science
File Size : 48. 55 MB
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Everyone is familiar with the amazing performance of a modern laptop, powered by more than a billion nanotransistors, each having an active region that is barely a few hundred atoms long. These lectures, however, are about a less-appreciated by-product of the microelectronics revolution, namely the deeper understanding of current flow, energy exchange and device operation that it has enabled, which forms the basis for what we call the bottom-up approach. The book assumes very little background beyond linear algebra and differential equations, and is intended to be accessible to anyone in any branch of science or engineering. These lectures represent our attempt to make these lessons broadly accessible to those who are not experts in device physics or transport theory, and would like to keep it that way. At the same time, we hope the experts too will enjoy taking a fresh new look at their favorite subject, emphasizing fundamental insights of general validity.

Principles Of Inorganic Materials Design

Author : John N. Lalena
ISBN : 0470567538
Genre : Technology & Engineering
File Size : 54. 9 MB
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Unique interdisciplinary approach enables readers to overcome complex design challenges Integrating concepts from chemistry, physics, materials science, metallurgy, and ceramics, Principles of Inorganic Materials Design, Second Edition offers a unique interdisciplinary approach that enables readers to grasp the complexities of inorganic materials. The book provides a solid foundation in the principles underlying the design of inorganic materials and then offers the guidance and tools needed to create specific materials with desired macroscopic properties. Principles of Inorganic Materials Design, Second Edition begins with an introduction to structure at the microscopic level and then progresses to smaller-length scales. Next, the authors explore both phenomenological and atomistic-level descriptions of transport properties, the metal?nonmetal transition, magnetic and dielectric properties, optical properties, and mechanical properties. Lastly, the book covers phase equilibria, synthesis, and nanomaterials. Special features include: Introduction to the CALPHAD method, an important, but often overlooked topic More worked examples and new end-of-chapter problems to help ensure mastery of the concepts Extensive references to the literature for more in-depth coverage of particular topics Biographies introducing twentieth-century pioneers in the field of inorganic materials science This Second Edition has been thoroughly revised and updated, incorporating the latest findings and featuring expanded discussions of such key topics as microstructural aspects, density functional theory, dielectric properties, mechanical properties, and nanomaterials. Armed with this text, students and researchers in inorganic and physical chemistry, physics, materials science, and engineering will be equipped to overcome today's complex design challenges. This textbook is recommended for senior-level undergraduate and graduate course work.

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