Bose gas in disordered, finite-layered systems

Disorder effects in the thermodynamic properties of a Bose gas are analyzed. The gas is confined within a layered box of size $L$ in the z-direction and infinite in the other two directions. The layers are first modeled by a periodic array of $M$ Dirac delta-functions of equal intensity. We investigate the effects on the specific heat, energy and entropy when a random set of vacancies is introduced in the layered array. A dramatic increase in the maximum of the specific heat is observed when the system has a $0.1$ to $0.2$ fraction of random vacancies compared to the original, periodic array and this maximum, which is reminiscent of a Bose-Einstein condensation for an infinite array, occurs at a higher temperature.