标题： 非线性无序Klein-Gordon晶格中时空混沌的频率图分析 显示英文标题

标题： Frequency map analysis of spatiotemporal chaos in the nonlinear disordered Klein-Gordon lattice

摘要： 我们通过计算每个振子运动的基本频率随时间的变化，研究了一维非线性无序Klein-Gordon格子中初始局域化能量激发的混沌演化特性。 我们关注所谓的“弱混沌”和“强混沌”扩展区域的动力学 [2010, EPL 91 30001]，在这些区域中Anderson局域化被破坏。 基于基本频率的大范围变化表示强烈的混沌行为这一事实，我们表明在两种情况下，混沌在波包中心区域更为强烈，同时该区域的能量含量也更高，而波包边缘的振子直到它们获得足够的能量成为高度激发部分之前表现出规则运动。 最终，尽管波包扩展时激发位点的数量增加，但混沌振子的百分比保持几乎不变，但高度混沌位点的比例随时间减少。 我们表明，在强混沌区域中，波包边缘的规则运动区域的范围比弱混沌情况要小得多。 此外，我们发现，在强混沌区域中，波包的混沌成分不仅比弱混沌区域更广泛，而且强混沌振子的比例也高得多。 弱混沌和强混沌区域之间的另一个重要区别是，在后者的情况下，即使在演化的早期阶段，也被激发的频率数量显著更大。 此外，我们的计算证实了在所谓的“自 trapping”区域中，大部分波包保持局域化时，基本频率会偏离线性系统的正常模频率带。 显示英文摘要

摘要： We study the characteristics of chaos evolution of initially localized energy excitations in the one-dimensional nonlinear disordered Klein-Gordon lattice of anharmonic oscillators, by computing the time variation of the fundamental frequencies of the motion of each oscillator. We focus our attention on the dynamics of the so-called `weak' and `strong chaos' spreading regimes [2010, EPL 91 30001], for which Anderson localization is destroyed. Based on the fact that large variations of the fundamental frequencies denote strong chaotic behavior, we show that in both regimes chaos is more intense at the central regions of the wave packet, where also the energy content is higher, while the oscillators at the wave packet's edges exhibit regular motion up until the time they gain enough energy to become part of the highly excited portion of the wave packet. Eventually, the percentage of chaotic oscillators remains practically constant, despite the fact that the number of excited sites grows as the wave packet spreads, but the portion of highly chaotic sites decreases in time. We show that the extent of the zones of regular motion at the edges of the wave packet in the strong chaos regime is much smaller than in the weak chaos case. Furthermore, we find that in the strong chaos regime the chaotic component of the wave packet is not only more extended than in the weak chaos one, but in addition the fraction of strongly chaotic oscillators is much higher. Another important difference between the weak and strong chaos regimes is that in the latter case a significantly larger number of frequencies is excited, even from the first stages of the evolution. Moreover, our computations confirmed the shifting of fundamental frequencies outside the normal mode frequency band of the linear system in the case of the so-called `selftrapping' regime where a large part of the wave packet remains localized.