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We continue our study of the quantum optics of a single photon interactingwith a system of two level atoms. In this work we investigate the case of aperiodic arrangement of atoms. We provide a general structure theoremcharacterizing the band functions of this problem, which comprise the spectrumof the associated Hamiltonian. Additionally, we study atomic densities arisingas periodically arranged scaled inclusions. For this family of examples, weobtain explicit asymptotic formulas for the band functions.

Nonlocal PDEs and quantum optics: band structure of periodic atomic sytems