Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Nonlinear dynamics, synchronization and chaos I

DY 3.5: Vortrag

Montag, 23. März 2009, 12:00–12:15, ZEU 118

Spreading of wavepackets in one dimensional disordered chains - I. Different dynamical regimes — •Charalampos Skokos, Sergej Flach, and Dmitry Krimer — Max Planck Institute for the Physics of Complex Systems, Nothnitzer Str. 38, D-01187 Dresden, Germany

We present numerical results for the spatiotemporal evolution of a wavepacket in quartic Klein-Gordon (KG) and disordered nonlinear Schrödinger (DNLS) chains, having equivalent linear parts. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). In the presence of nonlinearity we find three different dynamical behaviors depending on the relation of the nonlinear frequency shift δ (which is proportional to the system’s nonlinearity) with the average spacing Δ λ of eigenfrequencies and the spectrum width Δ (Δ λ <Δ) of the linear system. The dynamics for small nonlinearities (δ < Δ λ) is characterized by localization as a transient, with subsequent subdiffusion (regime I). For intermediate values of the nonlinearity, such that Δ λ < δ <Δ the wavepackets exhibit immediate subdiffusion (regime II). In this case, the second moment m₂ and the participation number P increase in time following the power laws m₂ ∼ t^α, P ∼ t^α/2. We find α=1/3. Finally, for even higher nonlinearities (δ > Δ) a large part of the wavepacket is selftrapped, while the rest subdiffuses (regime III). In this case P remains practically constant, while m₂ ∼ t^α.