Non-additive model for specific heat of electrons

By using non-additive Tsallis entropy we demonstrate numerically that one-dimensional quasicrystals, whose energy spectra are multifractal Cantor sets, are characterized by an entropic parameter, and calculate the electronic specific heat, where we consider a non-additive entropy Sq. In our method we consider an energy spectra calculated using the one-dimensional tight binding Schrödinger equation, and their bands (or levels) are scaled onto the [0,1] interval. The Tsallis' formalism is applied to the energy spectra of Fibonacci and double-period one-dimensional quasiperiodic lattices. We analytically obtain an expression for the specific heat that we consider to be more appropriate to calculate this quantity in those quasiperiodic structures.