Chaos and Anderson Localization in Disordered Classical Chains: Hertzian vs FPUT models

A Ngapasare (1) , Georgios Theocharis (1) , Olivier Richoux (1) , Ch. Skokos (2, 3) , V. Achilleos (1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans
2 Department of Mathematics and Applied Mathematics [Cape Town]
3 MPI-PKS - Max Planck Institute for the Physics of Complex Systems

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.

Domaines: Dynamique Chaotique [nlin.CD]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

A Ngapasare, Georgios Theocharis, Olivier Richoux, Ch. Skokos, V. Achilleos. Chaos and Anderson Localization in Disordered Classical Chains: Hertzian vs FPUT models. Physical Review E , 2019. ⟨hal-02370309⟩