Properties of localized vibrational modes on fractal structures

A. Petri

Physica A: Statistical Mechanics and its Applications, 1992, vol. 185, issue 1, 166-173

Abstract: The harmonic dynamics of a random fractal structure is characterized by the existence of localized modes (fractons). Usually the study of these modes refers to the determination of their localization lengths; within these lengths the amplitudes of modes show large fluctuations, which are usually neglected by considering average properties. In the present work we focus on the scaling properties of these fluctuations; we find that normal modes of a percolating network possess multifractal behaviour. The analysis of spatial properties of a large number of modes, also belonging to different realizations of the disordered lattice, shows that the cumulant generating function τ(q) of the measure (the square site amplitude) exhibits anomalous scaling, and a dependence on the energy of vibrations.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:185:y:1992:i:1:p:166-173

DOI: 10.1016/0378-4371(92)90452-V

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