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 BoseEinstein condensation (BEC) critical temperature Tc that decreases monotonically from the 3D ideal boson gas (IBG) value T0 as the strength of confinement P0 is increased while keeping the channel's cross section, axay constant. In contrast, Tc is a non-monotonic function of the cross-section area for fixed P0. 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 Nb3Sn.

Trapping Effect of Periodic Structures on the Thermodynamic Properties of a Fermi Gas

“…The specific heat of a boson gas has been reported in Ref. [13][14][15] where we can observe a transition from a 3D system to a 2D one, which becomes evident for certain parameter values and sufficiently high temperatures. At this point is where the advantages of summing over a great amount of allowed energy bands shows its relevance.…”

“…Meanwhile, as P 0 → ∞, we have a fermion gas inside a two dimension structure, giving a zero chemical potential at T /T F = 1.44, as expected. We make a similar procedure for the boson an fermi gases inside a multitube structure, the first one being reported in 15 . But for a fermion gas we start from the equation…”

Bose gas with generalized dispersion relation plus an energy gap

“…It is well known that for a 3D homogeneous IBG of permanent particles there is a BEC critical temperature T c different from zero such that for T<T c a large portion of all particles are on the ground state forming a BEC [10], this phenomenon is not observed at temperatures different from zero for 2D or 1D Bose gases, whether spatially homogeneous [11] or within spatially periodic structures (multilayeres, multitubes, ...), as can be deduced from results reported in [12] and [13], where external periodic potentials acting on a 3D IBG always decresed its BEC critical temperature below that of a free IBG. Also, it is known that external uniform potentials [14][15][16][17][18] can change the particle energy-momentum relation of an IBG and, as a consequence, the dimensionality where BEC can exist as well as the magnitude of its critical temperature.…”

Finite Size Effect on the Specific Heat of a Bose Gas in Multi-filament Cables

“…The main difference with respect to the infinite case [10] 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.…”

“…Second, a square array of 121 penetrables filaments of infinite length inside a hard tube is studied, this array in created by set M = 10 (11 × 11 filaments). The third system analyzed is a infinite periodic array of filaments of infinite length [10] (infinite number of filaments). We remark that the filaments composing the three different systems have the same finite cross section area (a/λ 0 ) 2 and infinite length.…”