Universal features of hydrodynamic Lyapunov modes in extended systems with continuous symmetries.
Numerical and analytical evidence is presented to show that hydrodynamic Lyapunov modes (HLMs) do exist in lattices of coupled Hamiltonian and dissipative maps. More importantly, we find that HLMs in these two classes of systems are different with respect to their spatial structure and their dynamical behavior. To be concrete, the corresponding dispersion relations of Lyapunov exponent versus wave number are characterized by lambda approximately k and lambda approximately k2, respectively. The HLMs in Hamiltonian systems are propagating, whereas those of dissipative systems show only diffusive motion. Extensive numerical simulations of various systems confirm that the existence of HLMs is a very general feature of extended dynamical systems with continuous symmetries and that the above-mentioned differences between the two classes of systems are universal in large extent.
Yang
Hong-liu
HL
Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany. hongliu.yang@physik.tu-chemnitz.de
Radons
Günter
G