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

2023/11/21 by Erik Orvehed Hiltunen, Joseph Kraisler, Hiltunen, Erik Orvehed +5 · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2311.12632

Abstract

We continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a general structure theorem characterizing the band functions of this problem, which comprise the spectrum of the associated Hamiltonian. Additionally, we study atomic densities arising as periodically arranged scaled inclusions. For this family of examples, we obtain explicit asymptotic formulas for the band functions.

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