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A simple model shows how it is possible to create a gap in the vibrationalspectrum of a one-dimensional lattice. The proposed model is a host-guest chainhaving, instead of point-like masses connected by spring, massive cages hostingparticles inside. We imagine the cage as a rigid box containing a mass linkedby a spring to the box inner wall. The presence of guests creates an energy gapin the dispersion of vibrational frequencies. The gap is about the internalresonance of the mass hidden in the cage.

Vibrations of a one-dimensional host-guest system