In the semi-classical limit the relativistic quantum mechanics of a stationary beam of counter-streaming (negatively charged) electrons and one species of positively charged ions is described by a nonlinear system of finite-temperature Thomas–Fermi equations. In the high temperature / low density limit these Thomas–Fermi equations reduce to the (semi-)conformal system of Bennett equations discu...

We detail the cooling mechanisms of a Fermionic strontium-87 gas in order to study its evolution under non-Abelian gauge field. In contrast our previous work reported Ref. [1], we emphasize here on finite temperature effect gas. addition, provide characterization for efficiency atoms loading cross-dipole trap, quantitative performance evaporative cooling, and degenerate Fermi using Thomas-Fermi...

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equat...

First, the Thomas-Fermi-Amaldi (TFA) equation was formulated with a newly derived condition to remove the singularities at the nuclei, which coincided with the molecular cusp condition. Next, the collocation method was applied to the TFA equation using the grid-based density functional theory. In this paper, the electron densities and the radial probabilities for specific atoms (He, Be, Ne, Mg,...

For the generalized Thomas–Fermi differential equation (|x|x) = q(t)|x|x, it is proved that if 1 6 α < β and q(t) is a regularly varying function of index μ with μ > −α − 1, then all positive solutions that tend to zero as t → ∞ are regularly varying functions of one and the same negative index ρ and their asymptotic behavior at infinity is governed by the unique definite decay law. Further, an...

The homotopy analysis method (HAM) is sharpened to solve the Thomas–Fermi equation. Some techniques are employed, including the use of asymptotic analysis to introduce proper transformation, and the use of optimal initial guess and optimal auxiliary linear operator to accelerate the convergence of homotopy approximations. The optimal convergence control parameters are determined by the minimum ...

As stated at the beginning of section 2.7 the total energy is a key function describing the basic physical and chemical properties of materials: the ground state. It consists of both kinetic (describing motion) and potential energy parts. To make a theoretical model realistic it is very important to incorporate all important contributions to both the parts of the total energy. In view of the bi...

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas-Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactl...

This paper presents the Thomas-Fermi approach generalized to consider the particle correlations in many-body systems with non-Coulomb interaction potentials. The key points of the generalization consist in using integral formulation and extracting the pair distribution function. The latter has been found to obey the integral equation which, in the classical limit, is reduced to the well-known e...