The perturbed Maxwell operator as pseudodifferential operator
Documenta mathematica, Tome 19 (2014), pp. 63-101
As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in d=3 can be seen as a pseudodifferential operator. This necessitates a better understanding of the periodic Maxwell operator M0. In particular, we characterize the behavior of M0 and the physical initial states at small crystal momenta k and small frequencies. Among other things, we prove that generically the band spectrum is symmetric with respect to inversions at k=0 and that there are exactly 4 ground state bands with approximately linear dispersion near k=0.
Classification :
35P99, 35Q60, 35Q61, 35S05, 78A48
Mots-clés : Maxwell equations, pseudodifferential operators, Maxwell operator, Bloch-Floquet theory
Mots-clés : Maxwell equations, pseudodifferential operators, Maxwell operator, Bloch-Floquet theory
@article{10_4171_dm_440,
author = {Giuseppe De Nittis and Max Lein},
title = {The perturbed {Maxwell} operator as pseudodifferential operator},
journal = {Documenta mathematica},
pages = {63--101},
year = {2014},
volume = {19},
doi = {10.4171/dm/440},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/440/}
}
Giuseppe De Nittis; Max Lein. The perturbed Maxwell operator as pseudodifferential operator. Documenta mathematica, Tome 19 (2014), pp. 63-101. doi: 10.4171/dm/440
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