Quantum Chaos and Mesoscopic Systems

Mathematical Methods in the Quantum Signatures of Chaos

By:

N.E. Hurt

Format:

Paperback / softback

Series:

Mathematics and its Applications

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Description

This is the first monograph to present a comprehensive treatment of the mathematical foundations of quantum chaos. Precise results in this area involve an exciting mixture of analytical number theory, zeta and L-functions, random matrix theory, scattering theory, the Selberg trace formula, and related global functional analysis. Many examples are presented including polygonal and standard billiards systems and models on the pseudosphere. The physics of both compact and finite volume systems are discussed, as well as systems in the presence of a magnetic field. Results on the spectra of Gutzwiller models for mesoscopic systems are discussed including questions of dissolving eigenvalues, simplicity of the spectra and exceptional eigenvalues. Relationships to isometric-isospectral questions in physics are discussed. Finally, applications of quantum chaos to recent results on mesoscopic physics are discussed, in particular transport properties in these devices. Starting from simple examples, the text leads the reader through the most recent work of Sarnak, Luo and coworkers on arithmetic chaos, Zelditch, Degli Esposti and coworkers on quantum ergodicity, Bleher and coworkers on integrable systems, Gutkin, Veech and coworkers on polygonal billiards, Sarnak, Phillips and coworkers on spectra of Gutzwiller models, Mueller and others on scattering theory, Berry, Keating, Steiner, Aurich, Bolte, Schmit, Bogomolny and coworkers on quantum chaos and Marcus Beenakker and coworkers on mesoscopic systems. Audience: This book will be of use to physicists, mathematicians, and engineers interested in quantum chaos and its applications to mesoscopic systems.

Release date NZ

December 5th, 2010

Author

N.E. Hurt

Audience

Professional & Vocational

Edition

Softcover reprint of hardcover 1st ed. 1997

Illustrations

XVI, 336 p.

Pages

336

Series

Mathematics and its Applications

Dimensions

170x244x18

ISBN-13

9789048148110

Product ID

11077887

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