Self-tuning behavior of vibrating smectic films

The wave equation that rules the drumhead oscillations of freestanding smectic films is similar to the two-dimensional Schrodinger equation. This makes vibrating smectic films the classical analog of appropriate quantum billiards. In particular, a rectangular smectic film carrying a very small inclusion, like a small metallic ball, is equivalent to a rectangular quantum billiard with a quasi-point-like scatterer. We point out that the ball, free to move in the plane of the film, tends to adjust its position as a function of the excitation frequency.