Wave chaos in the elastic disk.
Wave chaos in the elastic disk.
复制标题
弹性盘中的波动混乱。
DOI：
10.1103/physreve.66.066211
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
G. Tanner
中科院分区：
文献类型：
--
作者：
N. Søndergaard;G. Tanner
研究了平面各向同性体的弹性波方程与经典射线动力学之间的关系。我们研究，特别是，本征频率的弹性磁盘与自由边界和它们的连接到周期性射线内的圆形域。即使问题是可分离的，在边界处的波场的剪切和压力分量之间的波混合导致射线动力学中的有效随机部分。这引入了典型地与经典混沌相关联的现象，例如，周期轨道数量的指数增加。经典地，问题可以被分解成一个可积部分和一个简单的二进制马尔可夫过程。类似地，波动方程在高频极限下可以映射到量子图上。这一结果的水平统计的影响进行了讨论。基于本征模与散射解的内外对偶性，从散射矩阵导出了周期迹公式，并通过谱密度的傅里叶变换识别了周期轨道。
The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.