Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Poster I

DY 17.31: Poster

Dienstag, 26. Februar 2008, 16:00–18:00, Poster C

Hydrodynamic Lyapunov modes and strong stochasticity threshold in the dynamic XY model: an alternative scenario — •Hong-liu Yang and Günter Radons — Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany

Crossover from weak to strong chaos in high-dimensional Hamiltonian systems at the strong stochasticity threshold (SST) was anticipated manifesting a global transition in the geometric structure of the phase space. Our recent study of Fermi-Pasta-Ulam (FPU) models showed that corresponding to the transition of the system dynamics at the SST the scaling of the energy density dependence of all Lyapunov exponents exhibits a similar change as the largest one. Also the profiles of change of all Lyapunov exponents are identical apart from an energy density independent scaling factor. The current investigation of the dynamic XY model discovers an alternative scenario of change of the system dynamics at SSTs. Although the tendency of change of all Lyapunov exponents is similar the detailed profiles are different from each other except in the near-harmonic regime. Such a finding restricts the use of only crude indices such as the largest Lyapunov exponent and the Ricci curvatures to characterize the global transition in dynamics of high-dimensional Hamiltonian systems. Moreover, numerical simulations demonstrate the existence of HLMs in the dynamic XY model and show that there is a smooth transition in the energy density dependence of significance measures of HLMs corresponding to the crossover in Lyapunov exponents.