Effects of heterogeneity in site-site couplings for tight-binding models on scale-invariant structures

摘要

We studied the thermodynamic behaviors of non-interacting bosons and fermionstrapped by a scale-invariant branching structure of adjustable degree ofheterogeneity. The full energy spectrum in tight-binding approximation wasanalytically solved . We found that the log-periodic oscillation of thespecific heat for Fermi gas depended on the heterogeneity of hopping. Also, lowdimensional Bose-Einstein condensation occurred only for non-homogeneous setup.