The Perturbed Maxwell Operator as Pseudodifferential Operator
نویسندگان
چکیده
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. 2010 Mathematics Subject Classification: 35S05, 35P99, 35Q60, 35Q61, 78A48
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