Sensitivity to initial conditions of the self-trapping transition in C60 buckyballs with relaxing nonlinearity

We study the one-electron wavepacket dynamics in a C60 buckyball topology with a relaxing nonlinearity. The electron dynamics is considered to be governed by a discrete Schrödinger equation on which the nonlinear contribution obeys a Debye-like relaxation process. We follow the temporal evolution of the wavepacket and use the associated participation number to probe its spatial extension. By considering distinct initial conditions, we characterize the delocalization/self-trapping transition as a function of the nonlinear strength and relaxation time. We show that the phase-diagram exhibits a complex pattern of tongues signaling a re-entrant behavior of the transition which is strongly sensitive to the initial wavepacket distribution. The re-entrances become less prominent for initial conditions which are spatially distributed over opposite clusters.