Specific heat of multifractal energy spectra - art. no. 011104

Motivated by the self-similar character of energy spectra demonstrated for quasicrystals, we investigate the case of multifractal energy spectra, and compute the specific heat associated with simple archetypal forms of multif ractal sets as generated by iterated maps. We considered the logistic map a nd the circle map at their threshold to chaos. Both examples show nontrivia l structures associated with the scaling properties of their respective cha otic attractors. The specific heat displays generically log-periodic oscill ations around a value that characterizes a single exponent. the "fractal di mension," of the distribution of energy levels close to the minimum value s et to 0, It is shown that when the fractal dimension and the frequency of l og oscillations of the density of states are large, the amplitude of the re sulting log oscillation in the specific heat becomes much smaller than the log-periodic oscillation measured on the density of states.