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Thomas-Fermi approximation applied to calculation of equations of state and thermodynamic functions at high pressure from differential equations of statistical atom model
Asymptotic relations between Thomas-Fermi-Dirac and Thomas-Fermi atomic models
Asymptotic relations between Thomas-Fermi-Dirac and Thomas-Fermi atom models
Asymptotic relation between Thomas-Fermi-Dirac and Thomas-Fermi atom models for pressure with and without exchange, considering Coulomb contribution to energy
Use of new radiative opacities based on the hot Thomas-Fermi model of the atom yields a predicted solar neutrino flux which is still considerably larger than the flux observed in Davis's Cl-37 experiment.
Quantum point contacts (QPCs) are an essential component in mesoscopic devices. Here, in this work, we study the transmission of quantum Hall edge modes through a gate-defined QPC in monolayer graphene. We observe resonant tunneling peaks and a nonlinear conductance pattern characteristic of Coulomb-blockaded localized states. The in-plane electric polarizability reveals the states are localized at a classically unstable electrostatic saddle point. We explain this unexpected finding within a self-consistent Thomas-Fermi model, finding that localization of a zero-dimensional state at the saddle point is favored whenever the applied confinement potential is sufficiently soft compared to the Coulomb energy. Our results provide a direct demonstration of Coulomb-driven reconstruction at the boundary of a quantum Hall system.
The nuclear Thomas-Fermi model which is based on nuclear matter calculations has been successfully applied to the study of the bulk properties of nuclei. It is ideally suited for extrapolation into the region of very neutron-rich and of superheavy nuclei. It is therefore a valuable approach for r-process calculations as well as for the study of neutron star matter at subnuclear densities.
The emerging monochromatic fluxes and the B-V, V-I, J-H, and V-K color indices are presented for red degenerate stars with helium atmospheres which were calculated using an equation of state and opacities based on a hot Thomas-Fermi model of the helium gas. The effective temperature range is 4500-2500 K. It is found that although the emerging fluxes resemble blackbody curves, red degenerates emit more radiation than blackbodies in the short wavelength range and less in the long wavelength range. Thus, red degenerates appear bluer than blackbodies of the same temperature. The calculated colors of these models are compared to the colors of some of the coolest known non-DA degenerate stars. In particular it is found that the B-V and V-I colors of the cool white dwarf VB 11, whose temperature had been previously estimated to be higher than 4000 K, suggest a temperature of 3750 K. If this result is correct, then VB 11 is probably the coolest known white dwarf.
Atomic screening effects on nonrelativistic electron-atom bremsstrahlung radiation are investigated using a simple analytic solution of the Thomas-Fermi model for many-electron atoms. The Born approximation is assumed for the initial and final states of the projectile electron. The results show that the screening effect is important in the soft radiation region and is decreasing with increasing radiation. These results help provide correct information about the behavior of bound electrons in the target atom in bremsstrahlung processes.
The properties of two-dimensional (2D) electronic systems are often effectively controlled using electrostatic gating. The geometry of such field effect devices influences the effectiveness of the gate and the carrier density profile in the 2D device. Here, in this work, we analyze the gate-induced spatial variations in the lateral carrier density in patterned LaAlO 3 /SrTiO 3 devices. We model the electrostatics of the 2D interface using the Thomas-Fermi approximation and compute the gate-induced charge distribution at the interface. We show that the electric field lines generated by the gate are focused at the edges of the device, causing an increased depletion near its edges. This effect is accentuated in LaAlO 3 /SrTiO 3 due to the large, nonlinear dielectric constant of the substrate, and the large distance between the gate electrode and the interface. We experimentally demonstrate one consequence of this effect by directly imaging current distributions in gated heterostructures, finding that insulating regions nucleate at the edges of the device due to the gate. Our results suggest that device geometry and choice of dielectric materials control the charge distribution in 2D systems.
Comparison of evolutionary tracks, pulsation constants, and linearized pulsational-stability coefficients for stellar models applicable to the problems of classical Cepheids, whose structures were calculated using the Cox-Stewart (1965) opacities and a recently computed set of opacities. The latter are based on the hot 'Thomas-Fermi' statistical model of the atom for all elements heavier than hydrogen and helium; they contain larger helium and metals contributions, but a smaller hydrogen contribution than the former ones for the same chemical composition. The difference in metals contribution affects mainly the location and shape of the evolutionary tracks on the H-R diagram, while the difference in hydrogen and helium contributions has its greatest effect on the pulsational properties of the Cepheid models. From the comparison of evolutionary tracks it is concluded that: (1) the theoretical M/L relation for evolved giants is changed very little by using the second set of opacities; (2) Q-values for the fundamental mode of radial pulsation in Cepheid envelope models increase if the second set is used, but the classical mass discrepancy remains; and (3) the second set leads to pulsational-instability.
The radiation length in air, was studied. Calculations were finished and give new values for t sub o in atomic oxygen and nitrogen which are entirely free of dependence on the Thomas-Fermi approximate model. With the usual small corrections for atmospheric A and CO2, these give t sub o air = 37.15 g cm/2, in close agreement with a value recommended, but in contrast to t sub o air = 36.66 g cm/2 obtained using the Thomas-Fermi approximation.
The Multiphase Equation of State (MEOS) project works to produce high quality equation of state tables which are used in computationally intensive simulations of materials in different conditions. An equation of state table describes the state of matter under certain physical conditions such as pressure, volume, temperature, or internal energy. MEOS uses many different models and combinations thereof to produce accurate tables consisting of continuous smooth data, derivatives, and higher-order derivatives. Accurate and smooth data are important factors in producing precise simulations. This report focuses on improving the electron tables produced from Purgatorio and Thomas-Fermi data. Purgatorio data is extremely accurate but often jagged and discontinuous in the lower temperature and density region. Thomas-Fermi is a model that provides smooth data throughout. Together, this produces an EOS data table that is both accurate and smooth. This report describes the implementation of a new feature that allows users to define more detailed regions in the Purgatorio table to be replaced with Thomas-Fermi. As a result, MEOS can generate a table that is both more smooth and still accurate.
Apsidal-motion constants, k2, have been determined for models of homogeneous main-sequence stars constructed with the new 'Thomas-Fermi' opacities of Carson. These models are similar to those constructed with the 'hydrogenic' opacities of Cox and Stewart up to about 7 solar masses, but yield smaller values of k2 at higher masses. Nevertheless, the new theoretical constants are still systematically too large compared with most of the empirical constants known for members of well-observed binary systems. Uniform rotation is found to lower the theoretical constants only slightly. The effect of normal evolution during core hydrogen burning, however, produces good detailed agreement with observations. The primary of alpha Vir is probably evolving normally if Carson's opacities are adopted.
Brachman relations for generalized Thomas-Fermi and Thomas-Fermi-Dirac theories derived from Gibbs function and virial theorem
We derive the characteristic scales for physical quantities of dwarf galaxies, such as mass, size, acceleration, and angular momentum, within the self-interacting ultralight dark matter (ULDM) model. Due to the small mass of ULDM, even minor self-interactions can drastically alter these scales in the Thomas-Fermi limit. We suggest that these characteristic scales are connected to mysteries of observed galaxies. Oscillation of ULDM field can explain the current cosmological density of dark matter. Many cosmological constraints suggest that the energy scale $\tilde{m}$ for self-interacting ULDM is typically of the order $10~eV$, whereas the mass $m$ for the non-interacting case is around $10^{-21}~eV$. Self-interacting ULDM provides the better explanation for cosmological observations than the non-interacting case.
We obtain in closed analytic form, estimates for the thermodynamic properties of classical fluids with pair potentials of Yukawa type, with special reference to dense fully ionized plasmas with Thomas-Fermi or Debye-Hueckel screening. We further generalize the hard-sphere perturbative approach used for similarly screened two-component mixtures, and demonstrate phase separation in this simple model of a liquid mixture of metallic helium and hydrogen.
We report density functional theory has revolutionised our understanding of dense, strongly coupled systems in the condensed-matter limit. At elevated temperatures, such as those found in warm dense matter and dense plasma, the computational cost of calculating enough states to accurately describe a thermal ensemble of electrons is a major obstacle to practical Kohn-Sham calculations. This problem has recently been tackled from a number of approaches, including a plane-wave approximation for electrons at high energy. In this work, we demonstrate how the Thomas-Fermi density of states, equivalent to a local plane-wave approximation, can yield improved results for thermodynamic quantities, electron density profiles, and interatomic forces while requiring fewer states than existing methods.