Boson gas in a periodic array of tubes

TL;DR

This paper investigates the thermodynamic behavior of an ideal boson gas confined in a periodic array of channels, revealing how confinement and tunneling influence Bose-Einstein condensation and specific heat features, with implications for experimental systems.

Contribution

It introduces a model of boson gas in a periodic array of channels with delta-potentials, analyzing the effects of confinement on BEC critical temperature and thermodynamic properties.

Findings

Critical temperature decreases with increased confinement strength.

Specific heat shows maxima and minima related to confinement effects.

Dimensional crossover from 3D to 1D occurs with increased wall strength.

Abstract

We report the thermodynamic properties of an ideal boson gas confined in an infinite periodic array of channels modeled by two, mutually perpendicular, Kronig-Penney delta-potentials. The particle's motion is hindered in the x-y directions, allowing tunneling of particles through the walls, while no confinement along the z direction is considered. It is shown that there exists a finite Bose- Einstein condensation (BEC) critical temperature Tc that decreases monotonically from the 3D ideal boson gas (IBG) value $T_{0}$ as the strength of confinement $P_{0}$ is increased while keeping the channel's cross section, $a_{x}a_{y}$ constant. In contrast, Tc is a non-monotonic function of the cross-section area for fixed $P_{0}$. In addition to the BEC cusp, the specific heat exhibits a set of maxima and minima. The minimum located at the highest temperature is a clear signal of the confinement effect which occurs when the boson wavelength is twice the cross-section side size. This confinement is amplified when the wall strength is increased until a dimensional crossover from 3D to 1D is produced. Some of these features in the specific heat obtained from this simple model can be related, qualitatively, to at least two different experimental situations: $^4$He adsorbed within the interstitial channels of a bundle of carbon nanotubes and superconductor-multistrand-wires Nb$_{3}$Sn.