论文标题
Fermi-Pasta-Pasta-ulam-tsingou链中非线性正常模式的不稳定性动力学
Instability dynamics of nonlinear normal modes in the Fermi-Pasta-Ulam-Tsingou chains
论文作者
论文摘要
非线性正常模式是在非线性链中生存的周期性轨道，其不稳定性在多体哈密顿系统对热化的动力学中起着至关重要的作用。在这里，我们关注非线性模式的稳定性如何取决于扰动强度和系统大小，以观察它们在不同模型中是否具有相同的行为。为此，作为说明示例的说明，在固定边界条件下，在fermi-pasta-ulam-tsingou（fput） - $α$和 - $β$链条中，$ {n}/{2} $模式的不稳定性动力学都在系统地研究。应用Floquet理论，我们表明，对于两种模型，稳定时间$ t $作为扰动强度的函数$λ$都遵循相同的行为；即$ t \ propto（λ-λ_c）^{ - \ frac {1} {2}}} $，其中$λ_c$是不稳定性阈值。还获得了$λ_c$对$ n $的依赖性。 $ t $和$λ_c$的结果与直接分子动力学模拟获得的结果非常吻合。最后，简要讨论了不稳定性动力学对系统热化特性的影响。
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the ${N}/{2}$ mode in both the Fermi-Pasta-Ulam-Tsingou (FPUT) -$α$ and -$β$ chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time $T$ as a function of the perturbation strength $λ$ follows the same behavior; i.e., $T\propto(λ-λ_c)^{-\frac{1}{2}}$, where $λ_c$ is the instability threshold. The dependence of $λ_c$ on $N$ is also obtained. The results of $T$ and $λ_c$ agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed.
