Ngapasare A, Theocharis G, Richoux O, Skokos Ch, Achilleos V
Laboratoire d'Acoustique de l'Université du Maine, UMR CNRS 6613 Av. O. Messiaen, F-72085 LE MANS Cedex 9, France.
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
Phys Rev E. 2019 Mar;99(3-1):032211. doi: 10.1103/PhysRevE.99.032211.
We numerically investigate the dynamics of strongly disordered 1D lattices under single-particle displacements, using both the Hertzian model, describing a granular chain, and the α+β Fermi-Pasta-Ulam-Tsingou model (FPUT). The most profound difference between the two systems is the discontinuous nonlinearity of the granular chain appearing whenever neighboring particles are detached. We therefore sought to unravel the role of these discontinuities in the destruction of Anderson localization and their influence on the system's chaotic dynamics. Our results show that the dynamics of both models can be characterized by: (i) localization with no chaos; (ii) localization and chaos; (iii) spreading of energy, chaos, and equipartition. The discontinuous nonlinearity of the Hertzian model is found to trigger energy spreading at lower energies. More importantly, a transition from Anderson localization to energy equipartition is found for the Hertzian chain and is associated with the "propagation" of the discontinuous nonlinearity in the chain. On the contrary, the FPUT chain exhibits an alternate behavior between localized and delocalized chaotic behavior which is strongly dependent on the initial energy excitation.
我们使用描述颗粒链的赫兹模型和α + β费米-帕斯塔-乌拉姆-津古模型（FPUT），对单粒子位移下强无序一维晶格的动力学进行了数值研究。这两个系统之间最显著的差异在于，每当相邻粒子分离时颗粒链就会出现不连续非线性。因此，我们试图阐明这些不连续性在安德森局域化破坏中的作用及其对系统混沌动力学的影响。我们的结果表明，这两个模型的动力学都可以通过以下方式来表征：（i）无混沌的局域化；（ii）局域化和混沌；（iii）能量扩散、混沌和均分。发现赫兹模型的不连续非线性在较低能量下会触发能量扩散。更重要的是，发现赫兹链存在从安德森局域化到能量均分的转变，这与链中不连续非线性的“传播”有关。相反，FPUT链在局域化和非局域化混沌行为之间表现出交替行为，这强烈依赖于初始能量激发。
