Quasiperiodic Modulated-Spring Model

Abstract

We study the classical vibration problem of a chain with spring constants which are modulated in a quasiperiodic manner, {\it i. e.}, a model in which the elastic energy is ${\sum }_j{k}_j(u_{j-1}-u_j{)}^2$, where $k_j=1+\Delta cos[2\pi \sigma (j-1/2)+\theta ]$ and $\sigma$ is an irrational number. For $\Delta <1$, it is shown analytically that the spectrum is absolutely continuous, {\it i.e.}, all the eigen modes are extended. For $\Delta =1$, numerical scaling analysis shows that the spectrum is purely singular continuous, {\it i.e.}, all the modes are critical.

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References in corpus (1)

• Critical and bicritical properties of Harper's equation with next nearest neighbor coupling