Quantum Waveguides

This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research activity in this area and indicates ways in which the theory can develop further.

The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.

Provides a comprehensive and rigorous exposition of the theory of quantum waveguides Covers a wide range of mathematical problems arising in this young but actively developing area Includes an extensive bibliography Includes supplementary material: sn.pub/extras

Auteur

Pavel Exner is a Czech mathematical physicist.

Hynek Kovaík is an Assistant Professor in Mathematics at Università degli studi di Brescia. His areas of research cover problems in spectral theory of differential operators and functional analysis which arise from quantum physics.

Résumé
"The well-written and thorough monograph by Exner and Kovarík contains an excellent treatment of developments in the flourishing subject of quantum waveguides. ... The monograph is also highly recommended for those with a wider interest in quantum mechanics, since seeing how the concepts and mathematical methods of quantum mechanics need to be adapted to the case of waveguides is an engaging and instructive way to deepen one's understanding of them." (Evans M. Harrell II, Bulletin of the American Mathematical Society, Vol. 55 (2), April, 2018)

Contenu

Geometrically Induced Bound States.- Transport in locally perturbed tubes.- More about the waveguide spectra.- Dirichlet Layers.- Point Perturbations.- Weakly Coupled Bound States.- External Fields and Magnetic Transport.- Graph Limits of Thin Network Systems.- Periodic and Random Systems.- Leaky Waveguides.