论文标题
几何引起的弯曲波在薄翘曲的物理膜上的定位
Geometrically-induced localization of flexural waves on thin warped physical membranes
论文作者
论文摘要
我们认为弯曲波在几乎平坦的薄膜上传播，其无应力的状态是弯曲的。无应力配置由淬火高度场指定，其傅立叶组件是从具有功率法方差的高斯分布中得出的。高斯曲率将平面内伸展到平面外弯曲。在存在有效的随机电势的情况下，纯粹由几何形状确定的有效随机电势的情况下，整合更快的拉伸模式会产生波动的波动方程。我们表明，在长时间/长度上，起伏强度遵守扩散方程。发现扩散系数取决于频率，并且敏感到淬火高度场分布。最后，我们考虑了相干反向隔离校正的效果，从而产生了弱的定位校正，从而降低了与系统大小的对数成正比的扩散系数，并诱导了在猝灭高度场的大幅度下的定位跃迁。通过对强障碍制度的自洽扩展可以确认本地化过渡。
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.
