TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Strong and weak chaos in weakly nonintegrable many-body hamiltonian systems
JF  - Journal of statistical physics
N2  - 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.
KW  - Lyapunov exponent
KW  - Arnold diffusion
KW  - Chaos spreading
Y1  - 2011
U6  - https://doi.org/10.1007/s10955-011-0335-3
SN  - 0022-4715
VL  - 145
IS  - 5
SP  - 1256
EP  - 1274
PB  - Springer
CY  - New York
ER  -