Specific heat anomalies associated with Cantor-set energy spectra

Connection between energy spectrum, self-similarity, and specific heat log-periodicity

“…As in the two-scale case, these scale factors will be the essential ingredients for a very good approximate description of the thermodynamics of the system. We point out that the fractals considered in this paper might also be analized in their outbound and complete versions (in the nomenclature of [9]). These variations, which can also be treated within our formalism, will give rise to a thermodynamics analogous to that described above.…”

“…In this paper we extend the analysis of [9] to the case of multi-scale spectra and present a theoretical connection between the structure of the spectrum and the corresponding thermodynamical properties. In particular, we make explicit the relationship between discrete scaleinvariance and log-periodic oscillations.…”

“…As in general these spectra tend to be quite complex, simple models have been studied to enlighten the thermodynamical specificities that such systems may display. Within this vein, we studied in [9] one of the simplest fractal spectra (the triadic Cantor set); there it was shown that the specific heat of such system exhibits a very particular behaviour: it oscillates log-periodically around a mean value which equals the fractal dimension of the spectrum.…”

Possible Implication of a Single NonextensivepTDistribution for Hadron Production in High-EnergyppCollisions

“…(40) to be a complex number 4 (see also Refs. [60,61]; more details on this phenomenon, including also discussion of its presence in recent AA data, can be found in [33]). …”

Tsallis Distribution Decorated with Log-Periodic Oscillation

“…It is is usually taken in the form [56]: Before proceeding any further, let us remember that such log-periodic oscillations are widely know in all situations in which one encounters power distributions. In fact, such behavior has been found in earthquakes [57,58], escape probabilities in chaotic maps close to a crisis [59], biased diffusion of tracers on random systems [60][61][62], kinetic and dynamic processes on random quenched and fractal media [63][64][65][66], when considering the specific heat associated with self-similar [67] or fractal spectra [68], diffusion-limited-aggregate clusters [69], growth models [70] or stock markets near financial crashes [71][72][73][74], to name only a few examples. However, in all of these cases, the basic distributions were a scale-free power laws, without any scale parameter (here T ) and without a constant term governing their X < nT behavior.…”