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

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


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About the Book

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.

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.


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Product Details
  • ISBN-13: 9789048154463
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 240 mm
  • No of Pages: 302
  • Returnable: N
  • Sub Title: From Spectral Resonances to Anderson Localization
  • ISBN-10: 9048154464
  • Publisher Date: 15 Dec 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 506 Mathematics and Its Applications
  • Width: 160 mm


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