Finite size effect on the specific heat of a Bose gas in multifilament cables

TL;DR

This paper investigates how finite size and filament structure in semi-infinite Bose gases affect their specific heat, revealing smoothed maxima instead of sharp phase transition signatures.

Contribution

It introduces a model for Bose gases in multifilament cables with finite cross sections, analyzing the impact on specific heat and Bose-Einstein condensation features.

Findings

Specific heat exhibits multiple maxima and minima with temperature.

Finite size effects smooth out the Bose-Einstein transition peak.

The peak associated with BEC becomes a maximum rather than a discontinuity.

Abstract

The specific heat for an ideal Bose gas confined in semi-infinite multifilament cables is analyzed. We start with a Bose gas inside a semi-infinite tube of impenetrable walls and finite rectangular cross section. The internal filament structure is created by applying to the gas two, mutually perpendicular, Kronig-Penney delta-potentials along the tube cross section, while particles are free to move perpendicular to the cross section. The energy spectrum accessible to the particles is obtained and introduced into the grand potential to calculate the specific heat of the system as a function of temperature for different values of the periodic structure parameters such as: the cross section area, the wall impenetrability and the number of filaments. The specific heat as a function of temperature shows at least two maxima and one minimum. The main difference with respect to the infinite case is that the peak associated with the BE condensation becomes a smoothed maximum or in other words, there is not a jump in the specific heat derivative, whose temperature no longer represents a critical point.