Acoustic-wave propagation in quasiperiodic, incommensurate, and random systems.
Acoustic-wave propagation in quasiperiodic, incommensurate, and random systems.
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准周期、不通约和随机系统中的声波传播。
DOI：
10.1103/physrevb.38.8067
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
Birman
中科院分区：
文献类型：
--
作者：
Lu;Birman
我们研究了准周期、无公度和随机调制的一维系统中的声波传播。在短波长的限制，我们发现，如果初始脉冲是窄的（与几个晶格间距的顺序的空间扩展），脉冲是本地化的准周期系统的情况下，一个随机系统。这一结果表明，在短尺度下，准周期系统类似于随机系统。因此，那些不依赖于长程有序的输运性质应该在准晶和非晶金属玻璃中表现相似，与实验结果一致。另一方面，如果注入波的波长远大于晶格间距，我们发现当波矢满足布拉格条件时，准周期和无公度系统存在共振。在这种情况下，传播似乎是扩散的而不是传播的;也就是说，初始波的总能量并不像其他情况那样沿着链传播，而是均匀地分布在波前所经过的空间区域上。利用双模耦合理论和准周期系统的傅里叶谱，在长波极限下解析地解决了这个问题。分析结果与数值模拟结果完全一致。这表明，在长程尺度上，准周期有序不仅对晶体结构很重要，而且对那些依赖于长程有序的物理性质，如声波和微波传播也很重要。
We have studied acoustic-wave propagation in one-dimensional systems with quasiperiodic, incommensurate, and random modulation. In the short-wavelength limit we found that if the initial pulse is narrow (with spatial extension of the order of a few lattice spacings), the pulse is localized in a quasiperiodic system as in the case of a random system. This result shows that at short length scales a quasiperiodic system is similar to a random system. Therefore, those transport properties that do not depend on long-range order should behave similarly in quasicrystals and in an amorphous metallic glass, in agreement with experimental findings. On the other hand, if the injected wave has a wavelength much larger than the lattice spacing, we found that there are resonances for quasiperiodic and incommensurate systems when the wave vector satisfies the Bragg conditions. In this case propagation appears to be diffusive rather than propagative; namely, the total energy of the initial wave does not propagate along the chain as it does otherwise, but is homogeneously distributed over the region of space where the wave front passed. We solved the problem analytically in the long-wavelength limit in terms of two-mode-coupling theory and the Fourier spectrum of the quasiperiodic system. Analytical results are in full agreement with numerical simulations. These indicate that on a long-range scale quasiperiodic order is important not only for the crystal structure but also for those physical properties which depend on long-range order, such as acoustic-wave and microwave propagation.