Virovlyansky A L, Zaslavsky G M
Institute of Applied Physics, Russian Academy of Science, 603950 Nizhny Novgorod, Russia.
Chaos. 2005 Jun;15(2):23301. doi: 10.1063/1.1886645.
We consider wave propagation in a model of a deep ocean acoustic wave guide with a periodic range dependence. It is assumed that the wave field is governed by the parabolic equation. Formally the mathematical model of the wave guide coincides with that of a quantum system with time-dependent Hamiltonian. From the analysis of Floquet modes of the wave guide it is shown that there exists a "scarring" effect similar to that observed in quantum systems. It turns out that the segments of an unstable periodic ray trajectory may be distinguished in the spatial distribution of the wave field intensity at a finite wavelength. Besides the scarring effect, it is found that the so-called "stable islands" in the phase space of ray dynamics reveal themselves in the coarse-grained Wigner functions of the Floquet modes.
我们考虑在具有周期性距离依赖的深海声波导模型中的波传播。假设波场由抛物型方程控制。形式上，波导的数学模型与具有含时哈密顿量的量子系统的模型一致。通过对波导的弗洛凯模式的分析表明，存在一种类似于在量子系统中观察到的“疤痕”效应。结果表明，在有限波长下，波场强度的空间分布中可以区分出不稳定周期射线轨迹的片段。除了“疤痕”效应外，还发现射线动力学相空间中的所谓“稳定岛”在弗洛凯模式的粗粒化维格纳函数中表现出来。
