弯曲物理薄膜上弯曲波的几何诱导局部化
Geometrically-induced localization of flexural waves on thin warped physical membranes
摘要：
本文研究弯曲波在无应力状态为弯曲的近平薄膜上的传播。无应力配置指定的淬火高度场，其傅立叶分量是从高斯分布与幂律方差。高斯曲率将面内拉伸耦合到面外弯曲。在存在一个有效随机势的情况下，将更快的拉伸模式积分，得到波动方程，该波动方程完全由几何形状决定。我们表明，在长时间/长度，波动强度服从扩散方程。扩散系数被发现是频率依赖性和淬火的高度场分布敏感。最后，我们考虑相干后向散射校正的效果，产生一个弱的本地化校正，降低扩散系数成正比的系统大小的对数，并诱导本地化过渡在大幅度的淬火高度场。通过自洽扩展到强无序制度的本地化过渡确认。
英文摘要：
We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian distribution with power law variance. Gaussian curvature couples the in-plane stretching to out-of-plane bending. Integrating out the faster stretching modes yields a wave equation for undulations in the presence of an effective random potential, determined purely by geometry. We show that at long times/lengths, the undulation intensity obeys a diffusion equation. The diffusion coefficient is found to be frequency dependent and sensitive to the quenched height field distribution. Finally, we consider the effect of coherent backscattering corrections, yielding a weak localization correction that decreases the diffusion coefficient proportional to the logarithm of the system size, and induces a localization transition at large amplitude of the quenched height field. The localization transition is confirmed via a self-consistent extension to the strong disorder regime.
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