Decay of mesoscopically localized vibrational eigenstates in porous materials

The low-temperature decay of a vibrational eigenstate of a crystalline mesoscopic particle surrounded by other such particles of approximately the same size is considered. The decay time is determined by the anharmonicity and the coupling between adjacent mesoscopic particles. The coupling is assumed to be weak. Under some limiting conditions, discussed in the paper, for particles of a typical size of 50 Å the decay time at low temperatures can be several ms. The present theory may provide an explanation of the experimental findings by Kaplyanskii, Feofilov, and Zakharchenya who recently observed long-lived size-quantized vibrational states in porous ${\mathrm{Al}}_2{\mathrm{O}}_3$.