The anti-FPU problem.
We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.
Dauxois
Thierry
T
Laboratoire de Physique, UMR-CNRS 5672, ENS Lyon, 46 Allée d'Italie, 69364 Lyon Cédex 07, France.
Khomeriki
Ramaz
R
Piazza
Francesco
F
Ruffo
Stefano
S
D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*; D013997:Time Factors