The purpose of this paper is to prove that the spectrum of an isotropic Maxwell operator with electric permittivity and magnetic permeability that are periodic along certain directions and tending to a constant super-exponentially fast in the remaining directions is purely absolutely continuous. The basic technical tools is a new "operatorial'' identity relating the Maxwell operator to a vector-valued Schrödinger operator. The analysis of the spectrum of that operator is then handled using ideas developed by the same authors in a previous paper.
Publié le : 2004-06-22
Classification:
absolutely continuous spectrum,
Maxwell operator,
47A10 ; 35Q60,
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
@article{hal-00002142,
author = {Filonov, Nikolai and Klopp, Fr\'ed\'eric},
title = {Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00002142}
}
Filonov, Nikolai; Klopp, Frédéric. Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002142/