Localization and equipartition of energy in the β-FPU chain:: Chaotic breathers
Localization and equipartition of energy in the β-FPU chain:: Chaotic breathers
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DOI：
10.1016/s0167-2789(98)00107-9
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发表时间：
1998-10-01
期刊：
影响因子：
4
通讯作者：
Torcini, A
中科院分区：
文献类型：
--
作者：
Cretegny, T;Dauxois, T;Torcini, A
将最高频率模式作为初始条件，研究了 beta-FPU 链中的均分演化。在分析得出的能量阈值之上，这种区域边界模式被证明是调制不稳定的，并且会引起惊人的定位过程。自发产生的激励与移动精确呼吸解决方案具有很强的相似性。但它们的寿命是有限的，而且它们的动态是混乱的。这些混沌呼吸者能够非常有效地收集链条中的能量。因此，它们的尺寸会随着时间的推移而增长，并且可以传输大量的能量。这些特征可以通过分析 FPU 链的扰动精确呼吸器的动力学来解释。特别是，混沌呼吸者的李雅普诺夫谱和精确呼吸者的弗洛奎特谱之间的密切联系已经被发现。混沌呼吸体的出现可以通过高频声子的吸收得到令人信服的解释，而呼吸体的亚稳定性首次被识别。混沌呼吸器的寿命与系统达到均分所需的时间有关。事实证明，均分时间仅取决于系统能量密度 epsilon。此外，这样的时间在极限 epsilon --> 0 中发散为 epsilon(-2)，而在 epsilon --> 无穷大中则消失为 epsilon(-1/4)。 (C) 1998 Elsevier Science B.V.
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 metastabiljty 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 --> 0 and vanishes as epsilon(-1/4) for epsilon --> infinity. (C) 1998 Elsevier Science B.V.