**Contemporary Mathematics**

Volume: 339;
2003;
216 pp;
Softcover

MSC: Primary 35; 78; 81; 82;

Print ISBN: 978-0-8218-3286-8

Product Code: CONM/339

List Price: $69.00

AMS Member Price: $55.20

MAA member Price: $62.10

**Electronic ISBN: 978-0-8218-7929-0
Product Code: CONM/339.E**

List Price: $69.00

AMS Member Price: $55.20

MAA member Price: $62.10

# Waves in Periodic and Random Media

Share this page *Edited by *
*Peter Kuchment*

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

## Waves in Periodic and Random Media

- Contents v6 free
- Preface vii8 free
- Spectral properties of absorptive photonic crystals 112 free
- Regularity properties for the density of states of random Schrödinger operators 1526
- Spectral properties of Schrödinger operators with a strongly attractive δ interaction supported by a surface 2536
- Absolute continuity of the spectra of periodic waveguides 3748
- The Anderson metal-insulator transport transition 4354
- Theory and computation of scattering resonances of photonic microstructures 5970
- 1. Introduction and outline 6071
- 2. Maxwell's equations in a wave guide and the scalar approximation 6374
- 3. The resonance problem for microstructure waveguides 6576
- 4. Scattering resonances of the Schrödinger equation for high contrast and oscillatory potentials 6778
- 5. Multiple scales and homogenization expansion 6980
- 6. Numerical simulations for selected structures 7485
- 7. Implementation of homogenization expansion 7990
- 8. Summary and discussion 8899
- Appendix A. Calculations for simple layered structures 89100
- References 90101

- Asymptotic formulas for eigenvalues and eigenfunctions of periodic magnetic Schrödinger operators 91102
- On guided waves in photonic crystal waveguides 105116
- The design and photofabrication of random achromatic optical diffusers for uniform illumination 117128
- Resonance optical switch: calculation of resonance eigenvalues 141152
- High energy asymptotics of the density of states for certain periodic pseudo-differential operators in dimension one 171182
- On discrete spectrum in the gaps of a two-dimensional periodic elliptic operator perturbed by a decaying potential 185196
- On the principal eigenvalue of the Schrödinger operator with a scaled random potential 201212