Smectic liquid crystals can form free-standing films of large ratio surface-thickness which sometime permits us to view them as bidimensional systems. This viewpoint is useful to study the drum-head oscillations of these films. The frequency spectra of vibrating films is given by the wave equation which is similar to the 2D Schroedinger equation, which make them the classical analogue of the appropriate 'quantum billiards'. In particular, rectangular smectic films with a very small inclusion like a small ball cached by the film are equivalent to the rectangular quantum billiards with a quasi point-like scattering. A film of a dozen of layers can accommodate massif inclusions like a small steel ball. This ball tends to adjust its position on the film surface in function on the excitation frequency.
"Smectic films and quantum billiards", Proc. SPIE 3318, Liquid Crystals: Physics, Technology, and Applications, (1 February 1998); doi: 10.1117/12.300006; https://doi.org/10.1117/12.300006