Relaxational Fractons in Hopping Conduction on Fractal Lattice

On the basis of the relaxation mode theory, the hopping conduction on fractal lattices is investigated by the direct use of a set of eigenvalues and eigenstates for the relaxational fractons, where the relaxational fracton is a hopping version of the vibrational fracton. The obtained conductivity formula gives us full information over all the frequency and temperature range. Especially at a frequency and temperature range, its frequency-dependence is identical to the result derived by Alenxander and Orbach for fractal and percolation lattices. This scheme of dealing with the relaxational fractons is quite useful for the study of dynamical properties in the hopping conduction: the quasi-elastic light scattering and ultrasonic attenuation are also discussed on the same ground.