Bose gas in disordered, finite-layered systems

TL;DR

This study investigates how disorder and vacancies in layered structures affect the thermodynamic properties of an ideal Bose gas, revealing significant changes in specific heat behavior and transition temperatures.

Contribution

It introduces a model for disordered layered systems and analyzes the impact of structural and compositional disorder on Bose gas thermodynamics, highlighting the effects of layer depletion.

Findings

Disorder does not significantly alter thermodynamic properties.

Depletion of 10-20% of layers increases the specific heat maximum.

Maximum of specific heat shifts to higher temperatures with layer depletion.

Abstract

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.