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

Abstract

We report the thermodynamic properties of Bose and Fermi ideal gases immersed in periodic structures such as penetrable multilayers or multitubes simulated by one (planes) or two perpendicular (tubes) external Dirac comb potentials, while the particles are allowed to move freely in the remaining directions. Although the bosonic chemical potential is a constant for T < Tc, a non decreasing with temperature anomalous behavior of the fermionic chemical potential is confirmed and monitored as the tube bundle goes from 2D to 1D when the wall impenetrability overcomes a critical value. In the specific heat curves dimensional crossovers are very noticeable at high temperatures for both gases, where the system behavior goes from 3D to 2D and latter to 1D as the wall impenetrability is increased.

Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson–Fermion model

“…The unpaired electrons have the grand potential for an ideal Fermi gas immersed in a layered structure [31] Ω(T,…”

“…To include the effect of the layered structure of cuprates in the Boson-Fermion model, we calculate the BEC critical temperature and the thermodynamic properties for a system of non-interacting bosons immersed in a periodic multilayer array [29,30], simulated by an external Dirac comb potential along the perpendicular direction of the CuO 2 planes, while the Cooper pairs are allowed to move freely within the planes, with a linear energy-momentum dispersion relation [28]. The fermion counterpart is treated in a similar way [31] as the boson gas, subject to the same external potential. In this model, we assume that only a small fraction f of the initial N fermions available for pairing participate in the superconductivity at temperature T = T c and below, where the number of preformed pairs is large enough to achieve coherence independently of the mechanism by which the pairs are formed.…”

Thermodynamics of Low-Dimensional Trapped Fermi Gases

“…Truly, the significance of µ has motivated the discussion of its meaning and/or importance at different levels and contexts [41][42][43][44][45][46][47][48][49][50][51][52]. For the widely discussedtextbook-case, namely the three-dimensional IFG confined by a impenetrable box potential, the chemical potential results to be a monotonic decreasing function of the temperature, diminishing from the Fermi energy, E F , at zero temperature, to the values of the ideal classical gas for temperatures much larger than k −1 B ( 2 /mλ 2 T ), where k B is the Boltzmann's constant, is the Planck's constant divided by 2π, m the mass of the particle and λ T = 2π 2 /mk B T is the thermal wavelength of de Broglie, where T denotes the system's absolute temperature.…”