Abstract
Taking advantage of the close resemblance of Kirchhoff's laws and the equations of motion of isotropic phonons in a simply connected lattice, a device to directly observe the vibrational eigen-modes of a Penrose lattice was built with electric LC oscillators. The wave interference patterns observed in this network reveal key aspects concerning the localization of states, which has not been settled so far. There are truly extended eigen-states at low frequencies, and critically localized ones when their wavelength is of the order of the distance between neighbors in the lattice. The device allows the study of non-linear effects, when it is excited with higher voltages. These effects are analyzed by perturbation theory and the observed shifts of the eigen-frequencies are explained as a consequence of adding anharmonic terms to the Hamiltonian.
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