Gaussian random waves in elastic medium

Similar to Berry conjecture for quantum chaos we consider elastic analogue which incorporates longitudinal and transverse random waves. Based on that we derive the intensity correlation function of elastic displacement field. Comparison to numerics in a quarter Bunimovich stadium demonstrates a good agreement. We also consider nodal points (NPs) $u=0$, $v=0$ of the in-plane random vectorial displacement field $\mathbf u=(u,v)$. We derive the mean density and correlation function of NPs. Consequently, we derive the distribution of the nearest distances between NPs.