Dynamics of electron wave packet in a disordered chain with delayed nonlinear response

We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron–phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schrödinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.