Mathematical Physics of Quantum Wires and Devices: From Spectral Resonances to Anderson Localization by N.E. HurtMathematical Physics of Quantum Wires and Devices: From Spectral Resonances to Anderson Localization by N.E. Hurt

Mathematical Physics of Quantum Wires and Devices: From Spectral Resonances to Anderson Localization

byN.E. Hurt

Paperback | December 15, 2010

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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. Audience: This book will be of use to physicists, mathematicians and engineers interested in quantum wires, quantum devices and related mesoscopic systems.
Title:Mathematical Physics of Quantum Wires and Devices: From Spectral Resonances to Anderson LocalizationFormat:PaperbackDimensions:317 pages, 9.45 × 6.3 × 0 inPublished:December 15, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048154464

ISBN - 13:9789048154463

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Table of Contents

1. Quantum Wires and Devices. 2. Acoustic and Fluid Flow. 3. Trapped States in Bent Quantum Wires. 4. Mathematical Modeling and Quantum Devices. 5. Problems in Open Quantum Devices. 6. Anderson Localization. 7. Landau Models and the Quantum Hall Effect. 8. Selberg Trace Formula. 9. STF and Finite Volume Graphs. References. Index.