Bose gas in disordered, finite-layered systems

Disorder effects in the thermodynamic properties of a ideal Bose gas confined in a semi-infinite multi-layer structure %described by $M$ permeable barriers within a box of thickness $L$ and infinite lateral extent, are analyzed. The layers are first modeled by a periodic array of $M$ Dirac delta-functions of equal intensity. Then, we introduce structural and compositional disorder, as well as a random set of layer vacancies in the system to calculate the internal energy, chemical potential and the specific heat for different configurations. Whereas structural and compositional disorder does not reveal a significant change, a dramatic increase in the maximum of the specific heat is observed when the system is depleted a fraction of the order of $0.1$ to $0.2$ of random layers compared to the original, fully periodic array. Furthermore, this maximum, which is reminiscent of a Bose-Einstein condensation for an infinite array, occurs at higher temperatures.