Mathematical Physics of Quantum Wires and Devices: From Spectral Resonances to Anderson Localization: 506 (Mathematics and Its Applications, 506) - Hardcover

Hurt, N.E.

Hardcover

ISBN 10: 0792362888 ISBN 13: 9780792362883

Publisher: Springer, 2000

Synopsis

This monograph on quantum wires and quantum devices is a companion vol­ ume to the author's Quantum Chaos and Mesoscopic Systems (Kluwer, Dordrecht, 1997). The goal of this work is to present to the reader the mathematical physics which has arisen in the study of these systems. The course which I have taken in this volume is to juxtapose the current work on the mathematical physics of quantum devices and the details behind the work so that the reader can gain an understanding of the physics, and where possible the open problems which re­ main in the development of a complete mathematical description of the devices. I have attempted to include sufficient background and references so that the reader can understand the limitations of the current methods and have direction to the original material for the research on the physics of these devices. As in the earlier volume, the monograph is a panoramic survey of the mathe­ matical physics of quantum wires and devices. Detailed proofs are kept to a min­ imum, with outlines of the principal steps and references to the primary sources as required. The survey is very broad to give a general development to a variety of problems in quantum devices, not a specialty volume.

About this title

Synopsis

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. This book will be of use to physicists, mathematicians and engineers interested in quantum wires, quantum devices and related mesoscopic systems.

Edition details

• Publisher: Springer
• Publication date: 2000
• Language: English
• ISBN 10: 0792362888
• ISBN 13: 9780792362883
• Binding: Hardcover
• Number of pages: 317