Localization and delocalization in networks with varied connectivity

We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range coupling to all-to-all coupling. find fascinating interplay between interactions connectivity. In particular, we consider (i) harmonic, (ii) Jaynes-Cummings, (iii) Bose-Hubbard networks. start initial condition where one nodes is populated then let it evolve time. The time dynamics steady state characterize features (self-trapping) these large-scale For case harmonic networks, exact analytical results are obtained, demonstrate that connection shows self-trapping whereas finite-ranged delocalization. interacting cases (Jaynes-Cummings networks) investigated both via quantum semiclassical approach. obtain an interesting phase diagram when varies range strength interaction. investigate consequence imperfections cavity or qubit role inevitable disorder. Our relevant especially given recent experimental progress engineering systems long-range