The ideal Bose gas in non-integer dimensions and liquid⁴He in porous media

Abstract

Physical properties of the ideal Bose gas with non-integer dimensions between D = 2 and D = 3 are theoretically investigated. Calculation shows that there exists a hierarchy of condensation transitions with changing fractional dimensionality. The results obtained on the specific heat and the condensed density in non-integer dimensions are similar to those for liquid helium-4 in porous media. This results suggest that the geometrical factor may be important for the physical properties of liquid helium-4 in porous media.

Thermodynamics of Ideal Bose Gas Under Generic Power Law Potential in $d$-dimensions

“…But the order of phase transition for the trapped bosons in arbitrary is yet to be examined. Lot of efforts have been made in order to understand dimensional dependence of phase transition [3,9,11,12,17,20,21,29]. Thermodynamic as well as other properties are calculated in d-dimension for bosons as well as Fermions [30,31,32] and interesting conclusions such as equivalence relation between the Bose and Fermi gases in two dimensions is established [33].…”

Superfluid fraction of a charged boson fluid at non‐integer dimensions and superconducting films

“…Recently, it has been noted that porous media and films can be studied using non-integer dimensionality between 2 < D < 3 [12]. This study also revealed that several prominent features of porous media originate from dimensionality and detailed nature of mutual interaction plays a much less prominent role.…”

Investigation of Bose Condensation in Ideal Bose Gas Trapped under Generic Power Law Potential in d Dimension

“…al. [30] reported that the dimensionality contribution is a dominant factor to specify the behavior of BEC [30]. In general, there exists no discontinuity in C V at T = T C for free Bose gas in three dimensional space.…”

“…In this report, we give a special emphasis on specific heat at constant volume C V as well as its derivatives, which are the salient features to understand BEC [30].…”