Quasiperiodic Modulated-Spring Model

Details Quasiperiodic Modulated-Spring Model Quasiperiodic Modulated-Spring Model

1996-07-26

arxiv.org/abs/cond-mat/9607185v1

Physics

Condensed Matter

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Scientific paper

10.1143/JPSJ.65.3915

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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