STUDY OF THE SPECIFIC HEAT OF SYSTEMS WITH ENERGY SPECTRUM FRACTALAuthor:
Coronado Jiménez Ana Victoria.
Year:
2005.
University:
GRANADA [
www.ugr.es].
Place of defense: Facultad de Ciencias, Universidad de Granada.
Place of preparation: Departamento de Física Aplicada II, Universidad de Málaga.
Summary: The objective of the report presented is the systematic study of the specific heat of systems whose energy spectrum has a fractal structure. Such systems, and in particular the energy spectra with a fractal structure, have generated considerable interest recently, which has been reflected in the publication of numerous articles in reputable international journals. The starting point for this work is to study the specific heat of the energy spectrum obtained from the set of Cantor, whose properties are more remarkable: a) the specific heat to low temperatures presents periodic oscillations in the logarithm of the temperature, is say are oscillations log-periódicas T, and b) the value around which ranges is given by the fractal dimension of the whole Singer. From here, these results are reflected most outstanding and are widespread in the same spectra deterministic fractal wider set triádico Cantor, and even spectra multifractales, for which we have shown numerically that the specific heat is also an oscillating function periodically in the logarithm of the temperature around the spectral dimension of the whole, the value of which is dominated by the length of the first branch of the spectrum. This branch also controls the frequency of the oscillations. In addition, we studied the behavior of the amplitude and armonicidad of oscillations depending on the structure of the spectrum, and we found conditions for which the oscillatory regime disappears. Finally, we have achieved these results justify analytically. We have also studied spectra modeled with fractal-type random. In this case, we have proved that if the disorder spectrum random is small, specific heat for these spectra also owns oscillations log-periódicas around some mean value, which can be related to the deterministic fractal average, demonstrating so that fractal deterministic represents all fractal random used for the calculation. If the disorder introduced in the spectrum exceeds a certain critical value, the behavior of specific heat is totally chaotic. Then we conducted a study of the application of these techniques to study physical models related to fractals, and in particular we considered systems cuasiperiódicos Fibonacci and Thue-Morse in one dimension, both modeled with hamiltoniano high ligation , and whose energy spectrum has a fractal structure. Through numerical simulation have shown that the specific heat for these systems has properties similar to those found in the spectra modeled by simple deterministic fractal. Finally, we applied these techniques to the analysis of the calculation of specific heat spectra obtained for real, and in particular we have studied the energy spectrum obtained from the spectral lines of some chemical elements in the periodic table. We have shown that these spectra have multifractal structure and that only some of them existed relationship between the properties of the specific heat obtained with the fractal properties of their spectra.
