Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices
Bertin Many Manda, B. Senyange, Ch. Skokos
Abstract
We reveal the generic characteristics of wave-packet delocalization in two-dimensional nonlinear disordered lattices by performing extensive numerical simulations in two basic disordered models: the Klein-Gordon system and the discrete nonlinear Schr\"odinger equation. We find that in both models (a) the wave packet's second moment asymptotically evolves as ${t}^{{a}_{m}}$ with ${a}_{m}\ensuremath{\approx}1/5$ ($1/3$) for the weak (strong) chaos dynamical regime, in agreement with previous theoretical predictions [S. Flach, Chem. Phys. 375, 548 (2010)]; (b) chaos persists, but its strength decreases in time $t$ since the finite-time maximum Lyapunov exponent $\mathrm{\ensuremath{\Lambda}}$ decays as $\mathrm{\ensuremath{\Lambda}}\ensuremath{\propto}{t}^{{\ensuremath{\alpha}}_{\mathrm{\ensuremath{\Lambda}}}}$, with ${\ensuremath{\alpha}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\approx}\ensuremath{-}0.37$ ($\ensuremath{-}0.46$) for the weak (strong) chaos case; and (c) the deviation vector distributions show the wandering of localized chaotic seeds in the lattice's excited part, which induces the wave packet's thermalization. We also propose a dimension-independent scaling between the wave packet's spreading and chaoticity, which allows the prediction of the obtained ${\ensuremath{\alpha}}_{\mathrm{\ensuremath{\Lambda}}}$ values.