In this paper, we consider a compact manifold $(X,d)$ of negative curvature, and a family of semiclassical Lagrangian states $f_h(x) = a(x) e^{ \frac{ i}{ h} \phi(x)}$ on $X$. For a wide family of phases $\phi$, we show that $f_h$, when evolved by the semiclassical Schr\"odinger equation during a long time, resembles a random Gaussian field. This can be seen as an analogue of Berry's random waves conjecture for Lagrangian states.
Categories: math-ph math.AP math.MP