Dispersive effective behavior of high-contrast periodic media

Abstract: I will discuss my recent work with Y. Ershova and A. Kiselev, demonstrating that spectral problems for quantum graphs with rapidly oscillating high-contrast weights are asymptotically equivalent to “homogenised” models with energy-dependent interface conditions. We show that these asymptotically equivalent models are directly related (in the sense of Schur-Frobenius duality) to models for time-dispersive media, which in the time domain involve memory, and we characterize the corresponding time convolution kernels explicitly.