Dresden 2011 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 23: Nonlinear Waves/ Nonlinear Lattices
DY 23.3: Vortrag
Mittwoch, 16. März 2011, 14:45–15:00, ZEU 255
A generalized spreading conjecture in 2D nonlinear disordered media — •Joshua Bodyfelt and Sergej Flach — Max Planck Institut für Physik komplexer Systeme, Dresden
It is generally accepted that the presence of nonlinearity in a random lattice couples
the lattice’s localized Anderson modes. This coupling then allows mode resonances,
which in turn are responsible for spreading of initially compact, localized wavepackets.
The spreading is measurable via several moments, all showing a characteristic
subdiffusive behavior of tα, where α<1. Numerical investigations
confirm the validity of these measures, including a recent work [1] which discusses
the novel appearance of a dynamical crossover from strong to weak resonances (please see talk
by T.V. Laptyeva). The concept of a tunable nonlinearity (with power order of σ > 0) also
holds great interest [2], in that a critical power order is observed seperating
the two regimes of strong and weak resonances. However, these works mainly focus on 1D systems.
Within [3] a generalization was made to multidimensional lattices, with resonances on a
wavepacket’s surface (as opposed to those within the internal volume) being claimed as the main
mechanism for spreading. Here, we present for 2D lattices further numerical investigations into
this claim.
T.V. Laptyeva et al., Europhys. Lett. 91, 30001 (2010).
Ch. Skokos & S. Flach, Phys. Rev. E 82, 016208 (2010);
M. Mulansky & A. Pikovsky Europhys. Lett. 90, 10015 (2010);
H. Veksler et al., Phys. Rev. E, 80 037201 (2009).
S. Flach, Chemical Physics 375, 548 (2010).