Thomas–Fermi theory at the Planck scale: A relativistic approach

A new approach to the Thomas-Fermi boundary-value problem

“…In section 6, we have instead investigated the joint effect of relativistic, non-extensive and thermal effects in the Thomas-Fermi equation, and we have discovered the following approximate power-law behaviours for the solution of the modified Thomas-Fermi equation The original calculations of our work provide encouraging evidence in favour of the Thomas-Fermi equation being a valuable source of inspiration for understanding the wide range of modern applications [15,16,17,18,19] of atomic physics.…”

A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound

“…GUP models are significant as they introduce modifications in state equations and microscopic variables [46][47][48][49][50][51][52][53][54][55][56][57][58]. These models predict potential quantum gravity effects observable at various scales, with theories often approximating a minimum length scale akin to the Planck length (ℓ Pl = √ ℏG c 3 ), emphasizing quantum gravity's role in the cosmic framework [59][60][61][62][63][64][65].…”

On the reformulation of Thomas-Fermi model to make it compatible to the Planck-scale

“…The formal development of statistical physics to make it amenable to the Planck-scale is carried out in the articles [11][12][13][14][15][16]. In condensed matter physics the the generalization of uncertainty relation is used for the same purpose in the articles [17][18][19][20][21][22]. In black-hole physics also we find the extensive use of different types of deformed uncertainty algebra in the articles [23][24][25][26][27][28][29][30][31][32][33] to incorporate Planck-scale effect.…”

“…The recent work of Shebabi etal. [18,19] on the Thomas-Fermi(Thomas [38], Fermi [39]) are the fascinating extension of generalized uncertainty relation having quadratic momentum dependence. Thomas-Fermi (TF) model is a manyparticle statistical model that came up as a heuristic semi-classical method to describe the electrostatic potential and the charge densities in large atoms, metals, and in astrophysical objects such as neutron stars [40,41].…”

“…In [54], the correction is introduced at the operator level within the Hamiltonian and a perturbation technique is used to evaluate the energy of the system. But in our extension correction will be incorporated through the density of state-level as has been found in [18,19] following the formalism [55].…”