Superlocalized character of the viscous damping of fractons

Summary

The damping of the vibrations of very irregular discretized systems embedded in viscous fluid is studied in the particular case of the vibrations of a percolation cluster. We develop a formal description for the «regularity» of a vibrational mode. This permits us to measure numerically how the local fluctuations in the vibration amplitude increase the viscous damping. We find that a major part of the dissipation is localized in a small fraction of the next-nearest-neighbour pairs. This is a qualitative indication of the existence of a «localization within localization» of the dissipation. The fact that the regularity is found to be larger than that of a single localized state on a linear chain is qualitatively indicative of the structure of the percolation cluster made of blobs and red bonds.