Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 34: Poster
DY 34.31: Poster
Montag, 7. März 2005, 15:30–18:00, Poster TU D
Dynamics of hydrodynamic Lyapunov modes in coupled map lattices — •Hong-liu Yang and Günter Radons — Theoretische Physik I, Komplexe Systeme und Nichtlineare Dynamik, TU-Chemnitz
In our study of equal-time correlations of hydrodynamic Lyapunov modes in coupled map lattices, we found that there are two universality classes with different λ -k dispersion relations, λ ∼ k2 for coupled Hamiltonian maps and λ ∼ k for coupled dissipative maps. In this paper we perform numerical experiments to determine the form of the dynamic Lyapunov vector (LV) structure factors of coupled map lattices which provide detailed information on the LV dynamics. It is found that the dynamic LV structure factor for coupled circle maps has a single peak at ω =0 and can be well approximated by a single Lorentzian curve. This implies that the hydrodynamic Lyapunov modes of coupled circle maps are non-propagating and possess only diffusive thermo-motions. In contrast, in the dynamic LV structure factors of coupled standard maps, one observes two pronounced peaks located symmetrically at ± ω u. The spectra can be well approximated by three Lorentzian curves centered at ω =0 and ± ω u, respectively. The ω u-k dispersion relation takes the form ω u=cu· k. This implies that the hydrodynamic Lyapunov modes of coupled standard maps are propagating. These findings demonstrate that the HLMs in the two classes of models have different dynamical behavior besides their difference in the spatial structure. The existence of propagating Lyapunov modes in a system without continuous time-translational invariance calls for a new theoretical interpretation different from the one for many-particle systems.