Virovlyansky A. L., Zaslavsky G. M.
Institute of Applied Physics, Russian Academy of Science, 46 Ul'yanov Street, 603600 Nizhny Novgorod, Russia.
Chaos. 2000 Mar;10(1):211-223. doi: 10.1063/1.166486.
A ray-based approach has been considered for evaluation of the coarse-grained Wigner function. From the viewpoint of wave propagation theory this function represents the local spectrum of the wave field smoothed over some spatial and angular scales. A very simple formula has been considered which expresses the smoothed Wigner function through parameters of ray trajectories. Although the formula is ray-based, it nevertheless has no singularities at caustics and its numerical implementation does not require looking for eigenrays. These advantages are especially important under conditions of ray chaos when fast growing numbers of eigenrays and caustics are the important factors spoiling applicability of standard semiclassical approaches already at short ranges. Similar factors restrict applicability of some semiclassical predictions in quantum mechanics at times exceeding the so-called "logarithm break time." Numerical calculations have been carried out for a particular model of range-dependent waveguide where ray trajectories exhibit chaotic motion. These calculations have confirmed our conjecture that by choosing large enough smoothing scales, i.e., by sacrificing small details of the interference pattern, one can substantially enhance the validity region of ray theory. (c) 2000 American Institute of Physics.
一种基于射线的方法已被用于评估粗粒化维格纳函数。从波传播理论的角度来看，该函数表示在某些空间和角度尺度上平滑后的波场局部频谱。人们考虑了一个非常简单的公式，该公式通过射线轨迹的参数来表示平滑后的维格纳函数。尽管该公式基于射线，但它在焦散处没有奇点，并且其数值实现不需要寻找本征射线。在射线混沌的情况下，这些优点尤为重要，因为本征射线和焦散数量的快速增长是破坏标准半经典方法在短距离内适用性的重要因素。类似的因素有时会限制一些半经典预测在量子力学中的适用性，这种情况会超过所谓的“对数破裂时间”。已对一种距离相关波导的特定模型进行了数值计算，其中射线轨迹呈现混沌运动。这些计算证实了我们的猜想，即通过选择足够大的平滑尺度，也就是牺牲干涉图样的小细节，可以显著扩大射线理论的有效范围。（c）2000美国物理研究所。
