论文标题
使用测序的元容器变换来恢复近代的几何光学元件
Restoring geometrical optics near caustics using sequenced metaplectic transforms
论文作者
论文摘要
几何光学（GO）通常用于模拟弱不均匀培养基中的波浪传播，并在半经典极限下进行量子粒子运动。但是，GO预测波场在反射点附近，更普遍地是在苛性阶段。我们提出了一种新的GO公式，称为跨度几何光学（MGO），它不含这些奇异性，可以应用于任何线性波方程。 MGO使用波场的测序元容器变换，对应于射线相空间的符号转换，从而在新变量中消失了，并且GO被恢复了。使用MGO进行分析研究了通风的问题和量子谐波振荡器。在这两种情况下，与通常的GO解决方案不同，MGO解决方案都非常接近确切的解决方案，并且在截止方面保持有限。
Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and, more generally, at caustics. We present a new formulation of GO, called metaplectic geometrical optics (MGO), that is free from these singularities and can be applied to any linear wave equation. MGO uses sequenced metaplectic transforms of the wavefield, corresponding to symplectic transformations of the ray phase space, such that caustics disappear in the new variables, and GO is reinstated. The Airy problem and the quantum harmonic oscillator are studied analytically using MGO for illustration. In both cases, the MGO solutions are remarkably close to the exact solutions and remain finite at cutoffs, unlike the usual GO solutions.
