Effects of delayed nonlinear response on wave packet dynamics in one-dimensional generalized Fibonacci chains

We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth.