Delay Nonlinear Response Of A One-dimensional Quasi-periodic Wave Packet Diffusion System

In recent years, the electronic transport phenomena taking nonlinear systems attracted a lot of physicists’interest. When the electronic wave packet propagation in the crystal lattice, there will be some very interesting phenomenons in which one of the more well-known phenomenon called self-trapping. Usually, the nonlinearity produced by the electron phonon interaction is assumed to be instantaneous. However, this effective nonlinearity is limited by the finite response’ time of the medium, and the relaxation of the nonlinearity is known to have a deep influence on the electronic wave packet dynamics. Theoretical study found that delayed nonlinear response really has a great impact on wave packet dynamics behavior in uniform system and disordered systems, they also found some interesting phenomena. On the other hand, Shechtman et al discovery quasicrystals, and Marlin et al maked quasi-periodic superlattice of Fibonacci sequence on the experimental. Study on physical properties of quasicrystal system has become a hot topic in the field of condensed matter physics. In this paper, we advance in the study of effects of delayed nonlinear response on wave packet dynamics in one-dimensional quasiperiodic chains.Firstly, we investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrodinger 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 doesn’t grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates 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 doesn’t 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. We found that the nonlinear intensity does not affect the dynamic behavior of the wave packet at the same time. Then, we study numerically the spreading of an initially localized wave packet in a one-dimensional generalized Fibonacci (GF) chain with the effect of Debye-like relaxation of the nonlinearity. It is found that for first class of GF lattices with a weak on-site potential. Both the second moment and the participation number doesn’t grow with time in the regime of all delay times, which illuminates that wave packet is self-trapping. For a strong on-site potential, wave packet is self-trapping for short delay time. However, wave packet is localization for large delay time, that is, both the second moment and the participation number doesn’t grow with time in the a long-time limit. For second class of GF lattices with a weak on-site potential, wave packet is localization for all delay times. For a strong on-site potential, wave packet is still localization for short delay time.