Efeitos da topologia da rede de Apolônio sobre as propriedades termodinâmicas de gases quânticos não interagentes

Abstract

In this work, we have studied the properties of non-interacting quantum gases in the Apollonian network. By using the tight binding approach to compute the hamiltonian of the system, the energy spectrum and the density of states are computed. Due to the fractal characteristics of the Apollonian network, the structure of the energy bands presents a multifractal distribution. From the energy spectrum, the termodynamic properties of noninteracting quantum gases are studied. Our results show that the multifractal structure of the energy spectrum affects the behavior of fermions and bosons at low temperatures. In the particular case of the ideal gas of bosons, it is shown the existence of a Bose-Einstein condensation, with characteristics of a second order phase transition.