BEC and Dimensional Crossover in a Boson Gas Within Multi-slabs

Abstract

For an ideal Bose-gas within a multi-slabs periodic structure, we report a dimensional crossover and discuss whether a BEC transition at Tc = 0 disappears or not. The multi-slabs structure is generated via a Kronig-Penney potential perpendicular to the slabs of width a and separated by a distance b. The ability of the particles to jump between adjacent slabs is determined by the hight V0 and width b of the potential barrier. Contrary to what happens in the boson gas inside a zero-width multilayers case, where the critical temperature diminishes and goes up again as a function of the wall separation, here the Tc decreases continuously as the potential barrier height and the cell size a + b increase. We plot the surface Tc = 10 −6 showing two prominent regions in the parameters space, which suggest a phase transition BEC-NOBEC at T = 0. The specific heat shows a crossover from 3D to 2D when the height of the potential or the barrier width increase, in addition to the well known peak related to the Bose-Einstein condensation.

Universal Behavior of the BEC Critical Temperature for a Multi-slab Ideal Bose Gas

“…4 of Ref. [15]). The specific heat has a peak due to the Bose-Einstein condensation of the confined IBG at a critical temperature T c ≤ T 0 .…”

“…We previously found [15] that, when u 0 ≡ (2m(a + b) 2 /h 2 )V 0 1, the critical temperature is inversely proportional to the square root of this parameter. However, in order to observe separately the effects of the spatial period variation as well as the increasing of the potential height on the critical temperature, in this section, we find it convenient to replace u 0 byũ 0 ≡ (2mλ 2 0 /h 2 )V 0 which is period independent, and it depends exclusively on changes of the potential magnitude V 0 .…”

“…1 in Ref. [15] shows the energy spectrum, and the allowed energy bands, in terms of the dimensionless parameters u 0 = (2m(a + b) 2 /h 2 )V 0 ,ε z = (2m(a + b) 2 /h 2 )ε z and r = b/a, for r = 1. Pi squared times our energy unith 2 /2m(a + b) 2 is equivalent to the recoil energy of an 1D optical lattice formed by the interference of two counter-propagating light beams of wavelength equal to 2(a + b).…”