Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1997-09-18
Physica D, 121 (1998) 106
Physics
Condensed Matter
Statistical Mechanics
20 pages, Revtex - Submitted to Physica D
Scientific paper
10.1016/S0167-2789(98)00107-9
The evolution towards equipartition in the $\beta$-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally unstable and to give rise to a striking localization process. The spontaneously created excitations have strong similarity with moving exact breathers solutions. But they have a finite lifetime and their dynamics is chaotic. These chaotic breathers are able to collect very efficiently the energy in the chain. Therefore their size grows in time and they can transport a very large quantity of energy. These features can be explained analyzing the dynamics of perturbed exact breathers of the FPU chain. In particular, a close connection between the Lyapunov spectrum of the chaotic breathers and the Floquet spectrum of the exact ones has been found. The emergence of chaotic breathers is convincingly explained by the absorption of high frequency phonons whereas a breather's metastability is for the first time identified. The lifetime of the chaotic breather is related to the time necessary for the system to reach equipartition. The equipartition time turns out to be dependent on the system energy density $\epsilon$ only. Moreover, such time diverges as $\epsilon^{-2}$ in the limit $\epsilon \to 0$ and vanishes as $\epsilon^{-1/4}$ for $\epsilon \to \infty$.
Cretegny Thierry
Dauxois Thierry
Ruffo Stefano
Torcini Alessandro
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