Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure.

This book contains the proceedings of the research conference, "Waves in Periodic and Random Media". Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.

Readership

Graduate students and research mathematicians interested in mathematical physics and partial differential equations.

Table of Contents

• J. M. Combes, B. Gralak, and A. Tip -- Spectral properties of absorptive photonic crystals
• J.-M. Combes, P. D. Hislop, and F. Klopp -- Regularity properties for the density of states of random Schrödinger operators
• P. Exner -- Spectral properties of Schrödinger operators with a strongly attractive \(\delta\) interaction supported by a surface
• L. Friedlander -- Absolute continuity of the spectra of periodic waveguides
• F. Germinet and A. Klein -- The Anderson metal-insulator transport transition
• S. E. Golowich and M. I. Weinstein -- Theory and computation of scattering resonances of photonic microstructures
• Yu. Karpeshina -- Asymptotic formulas for eigenvalues and eigenfunctions of periodic magnetic Schrödinger operators
• P. Kuchment and B. Ong -- On guided waves in photonic crystal waveguides
• T. A. Leskova, A. A. Maradudin, E. R. Méndez, and J. Muñoz-Lopez -- The design and photofabrication of random achromatic optical diffusers for uniform illumination
• B. Pavlov and K. Robert -- Resonance optical switch: Calculation of resonance eigenvalues
• A. V. Sobolev -- High energy asymptotics of the density of states for certain periodic pseudo-differential operators in dimension one
• T. A. Suslina -- On discrete spectrum in the gaps of a two-dimensional periodic elliptic operator perturbed by a decaying potential
• V. V. Yurinsky -- On the principal eigenvalue of the Schrödinger operator with a scaled random potential