@article{MulanskyAhnertPikovskijetal.2011,
  author    = {Mulansky, Mario and Ahnert, Karsten and Pikovskij, Arkadij and Shepelyansky, Dima L.},
  title     = {Strong and weak chaos in weakly nonintegrable many-body hamiltonian systems},
  series = {Journal of statistical physics},
  volume    = {145},
  journal   = {Journal of statistical physics},
  number    = {5},
  publisher = {Springer},
  address   = {New York},
  issn      = {0022-4715},
  doi       = {10.1007/s10955-011-0335-3},
  pages     = {1256 -- 1274},
  year      = {2011},
  abstract  = {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 square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.},
  language  = {en}
}
@article{MulanskyAhnertPikovskij2011,
  author    = {Mulansky, Mario and Ahnert, Karsten and Pikovskij, Arkadij},
  title     = {Scaling of energy spreading in strongly nonlinear disordered lattices},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {83},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.83.026205},
  pages     = {4},
  year      = {2011},
  abstract  = {To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation, we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law.},
  language  = {en}
}