Abstract
Recent theoretical studies reveal the existence of so-called diabolical points in the energetic spectra of rectangular quantum billiards with a pointlike scatterer. The wave equation that rules the drum-head oscillations of free-standing smectic films is similar to the two-dimensional Schr\odinger equation, which makes vibrating smectic films the analogues of appropriate quantum billiards. In this Rapid Communication we study experimentally the diabolical points in a family of rectangular quantum billiards with an infinite scatterer via the resonance spectra of appropriate smectic films.
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