50 years of anderson localization

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50 Years Of Anderson Localization

Author : Elihu Abrahams
ISBN : 9789814299077
Genre : Science
File Size : 47. 85 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 : 66. 98 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 : UCLA:L0098871668
Genre : Physics
File Size : 79. 18 MB
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Introduction To Quantum Graphs

Author : Gregory Berkolaiko
ISBN : 9780821892114
Genre : Mathematics
File Size : 88. 7 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.

More Is Different

Author : N. Phuan Ong
ISBN : 0691088667
Genre : Science
File Size : 67. 9 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.

Quantum Phenomena In Mesoscopic Systems

Author : B. L. Alʹtshuler
ISBN : 1586033840
Genre : Science
File Size : 28. 33 MB
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This book is a snapshot of the vision shared by outstanding scientists on the key theoretical and experimental issues in Mesoscopic Physics. Quantum properties of electrons in solid state devices and transport in semiconducting and superconducting low-dimensional systems, are discussed, as well as the basis of quantum computing (entanglement, noise decoherence and read-out). Each chapter collects the material presented at a Varenna School course of last year, by leading experts in the field. The reader gets a flavor, how theorists and experimentalists are paving the way to the physical realization of solid state qubits, the basic units of the new logic and memory elements for quantum processing. He will be surprised in finding that mesoscopic solid state devices, which were invented just yesterday ( think of the Single Electron Transistor, or the Cooper Pair Box) are currently used as charge-sensing applications in the equipment of frontier research laboratories. These devices contribute as probing systems to produce evidence on still unsettled questions in topics like the metal-insulator transition in disordered two dimensional systems, quantum Hall conductance in heterostructures, or Kondo conductance in quantum dots.

Progress Of Theoretical Physics And Supplement

Author :
ISBN : UCAL:B4012062
Genre : Progress of theoretical physics
File Size : 45. 70 MB
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