Spreading of wave packets in disordered systems with tunable nonlinearity

We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{sigma} u_{l}$ for different values of $sigma$. We perform extensive numerical simulations where wave packets are evolved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{alpha}$. The dependence of the numerically computed exponent $alpha$ on $sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $sigma geq 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos, and observe destruction of Anderson localization in the packet tails for small values of $sigma$.