Quantum transport with long-range steps on Watts–Strogatz networks

We study transport dynamics of quantum systems with long-range steps on the Watts–Strogatz network (WSN) which is generated by rewiring links of the regular ring. First, we probe physical systems modeled by the discrete nonlinear schrödinger (DNLS) equation. Using the localized initial condition, we compute the time-averaged occupation probability of the initial site, which is related to the nonlinearity, the long-range steps and rewiring links. Self-trapping transitions occur at large (small) nonlinear parameters for coupling ϵ=−1 (1), as long-range interactions are intensified. The structure disorder induced by random rewiring, however, has dual effects for ϵ=−1 and inhibits the self-trapping behavior for ϵ=1. Second, we investigate continuous-time quantum walks (CTQW) on the regular ring ruled by the discrete linear schrödinger (DLS) equation. It is found that only the presence of the long-range steps does not affect the efficiency of the coherent exciton transport, while only the allowance of random rewiring enhances the partial localization. If both factors are considered simultaneously, localization is greatly strengthened, and the transport becomes worse.