2020/12/31 by Jianxing Du, Du, Jianxing, Xifeng Su +1
Physics and Astronomy · Materials Science · #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties #Rare-earth and actinide compounds
paper · pdf · doi:10.48550/arxiv.2012.15594
This article focuses on recent investigations on equilibria of the Frenkel-Kontorova models subjected to potentials generated by quasi-crystals. We present a specific one-dimensional model with an explicit potential driven by the Fibonacci quasi-crystal. For a given positive number θ, we show that there are multiple equilibria with rotation number θ, e.g., a minimal configuration and a non-minimal equilibrium configuration. Some numerical experiments verifying the existence of such equilibria are provided.