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

We study numerically the spreading of an initially localized wave packet in a one-dimensional uncorrelated disordered chain with a nonadiabatic electron-phonon interaction. The nonadiabatic electron-phonon coupling is taken into account in the time-dependent Schrödinger equation by a delayed cubic nonlinearity. In the adiabatic regime, Anderson localization is destroyed and a subdiffusive spreading of wave packet takes place by moderate nonlinearity. In the nonadiabatic regime, the dynamical behavior becomes obviously different. We find that short delay time suppresses delocalization strongly. However, large delay time gives a stronger exponent of spreading. An explanation of this delay induced effect is also discussed.