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Quasiperiodic Modulated-Spring Model

H. Hiramoto·Mahito Kohmoto
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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 $k_j=1+Δcos[2πσ(j-1/2)+θ]$ and $σ$ is an irrational number. For $Δ< 1$, it is shown analytically that the spectrum is absolutely continuous, {\it i.e.}, all the eigen modes are extended. For $Δ=1$, numerical scaling analysis shows that the spectrum is purely singular continuous, {\it i.e.}, all the modes are critical.

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H. Hiramoto, Mahito Kohmoto. 1996-07-26. Quasiperiodic Modulated-Spring Model. https://doi.org/10.1143/jpsj.65.3915

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