Physics Commons^™

Spectral Dimensionality Of Random Superconducting Networks, Anthony Roy Day, W. Xia, M. F. Thorpe

Anthony Roy Day

We compute the spectral dimensionality d-tilde of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d-tilde=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d-tilde=2d/(2-s/ nu ), where s is the superconducting exponent and nu the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d-tilde=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations …