Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices.

نویسندگان

  • M Romero-Bastida
  • Diego Pazó
  • Juan M López
چکیده

We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that, in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Comparison between covariant and orthogonal Lyapunov vectors.

Two sets of vectors, covariant Lyapunov vectors (CLVs) and orthogonal Lyapunov vectors (OLVs), are currently used to characterize the linear stability of chaotic systems. A comparison is made to show their similarity and difference, especially with respect to the influence on hydrodynamic Lyapunov modes (HLMs). Our numerical simulations show that in both Hamiltonian and dissipative systems HLMs...

متن کامل

Strong and Weak Chaos in Weakly Nonintegrable Many-Body Hamiltonian Systems

We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the squa...

متن کامل

Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices.

In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and Φ^{4} models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, bac...

متن کامل

Efficient time-series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices.

In this work we study the possibility of detecting the so-called strong stochasticity threshold (i.e., the transition between weak and strong chaos as the energy density of the system is increased) in anharmonic oscillator chains by means of the 0-1 test for chaos. We compare the result of the aforementioned methodology with the scaling behavior of the largest Lyapunov exponent computed by mean...

متن کامل

Diverging Fluctuations of the Lyapunov Exponents.

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-V...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 85 2 Pt 2  شماره 

صفحات  -

تاریخ انتشار 2012