Geodesic
The perturbed Maxwell operator as pseudodifferential operator
Documenta mathematica, Tome 19 (2014), pp. 63-101.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\Mper$. In particular, we characterize the behavior of $\Mper$ 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 : 35S05, 35P99, 35Q60, 35Q61, 78A48
Keywords: Maxwell equations, Maxwell operator, Bloch-Floquet theory, pseudodifferential operators 
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     author = {De Nittis, Giuseppe and Lein, Max},
     title = {The perturbed {Maxwell} operator as pseudodifferential operator},
     journal = {Documenta mathematica},
     pages = {63--101},
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     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a43/}
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De Nittis, Giuseppe; Lein, Max. The perturbed Maxwell operator as pseudodifferential operator. Documenta mathematica, Tome 19 (2014), pp. 63-101. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a43/