Boson gas in a periodic array of tubes

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.

9 pages, 10 figures, submitted

References in corpus (5)

• Phase transitions on the surface of a carbon nanotube
• Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
• Thermodynamic Evidence for Nanoscale Bose-Einstein Condensation in ^4He Confined in Nanoporous Media
• Dimensional crossover of a boson gas in multilayers
• Bose-Einstein condensation in multilayers

Cited by in corpus (2)

• Trapping effect of periodic structures on the thermodynamic properties of Fermi and Bose gases
• Finite size effect on the specific heat of a Bose gas in multifilament cables