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Revisiting the Thomas–Fermi potential for three-dimensional condensed matter systems
AbstractWe proposed a formally exact, probabilistic method to assess the validity of the Thomas–Fermi potential for three-dimensional condensed...
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Thomas-Fermi and Other Density-Functional Theories
The key idea in Thomas–Fermi theory and its generalizations is the replacement of complicated terms in the kinetic energy and electron–electron...
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On the Thomas–Fermi model at the noncommutative framework
In this paper, we present a generalized formulation of the Thomas–Fermi (TF), by considering the effect of a noncommutative space-time. Using the...
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Computational heuristics for solving nonlinear singular Thomas–Fermi equation with genetic exponential collocation algorithm
A novel approach of Genetic Exponential Collocation Algorithm (GECA) is reported for the solution of nonlinear singular Thomas–Fermi equation (TFE)...
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Stability of the Dust-Acoustic Solitons in the Thomas-Fermi Dense Magnetoplasma
An investigation is presented theoretically for the multi- dimensional instability of dust-acoustic solitary waves in the dense Thomas-Fermi...
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Nonlinear modulation of quantum electron acoustic waves in a Thomas–Fermi plasma with effects of exchange-correlation
The amplitude modulation of electron acoustic waves (EAWs) is investigated in an unmagnetized four-component quantum plasma containing dynamic cold...
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Signature of chaos and multistability in a Thomas-Fermi plasma
We propose a dynamical system governing from the nonlinear extension of the electrostatic ion-acoustic waves (IAWs) under the influence of external...
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Density Functional Theory for Two-Dimensional Homogeneous Materials
We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the...
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Probing M-theory with tetrahedron instantons
The duality between type IIA superstring theory and M-theory enables us to lift bound states of D0-branes and n parallel D6-branes to M-theory...
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A new heuristic computational solver for nonlinear singular Thomas–Fermi system using evolutionary optimized cubic splines
In the present work, a new stochastic computing technique based on evolutionary cubic spline method (CSM) is introduced for solving nonlinear...
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Analytical-Numerical Method for Calculating the Thomas-Fermi Potential
A method for computing the solution to the boundary value problem for the symmetric Thomas-Fermi model of a heavy atom or ion at zero absolute...
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Seven useful questions in density functional theory
We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context...
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Norm convergence of confined fermionic systems at zero temperature
The semi-classical limit of ground states of large systems of fermions was studied by Fournais et al. (Calc Var Partial Differ Equ 57:105, 2018). In...
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Electron–Electron Interaction
In this chapter the influence of the electron-electron (Coulomb) interaction on the electronic properties of solids is discussed. First the...
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Theoretical Model of Dense Plasmas
In the dawn of quantum mechanics, scientists had challenged to formulate the equation of many-electron system, such as atom and solid matter, just...
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Generic size dependences of pairing in ultrasmall systems: electronic nano-devices and atomic nuclei
We study the average and global pairing behaviours of electronic devices, like films, wires, and grains using semiclassical methods, such as Weyl and...
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Some problems in density functional theory
Though calculations based on density functional theory (DFT) are used remarkably widely in chemistry, physics, materials science, and biomolecular...
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6 Covariant Density Functional Theory and Applications to Finite Nuclei
Relativistic Hartree-Bogoliubov (RHB) theory is described in terms of a covariant density functional for a description of nuclear properties. Using...