We study the properties of elongated Bose-Einstein condensates. First, we show that the dimensions of the condensate after expansion differs from the 3D Thomas-Fermi regime. We also study the coherence length of such elongated condensates.

The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these frames can be explicitly constructed using either Killing or Killing-Yano tensors, the latter route chosen by Marck. For accelerated or geodesic circular orbits i...

ABSTRACT We have calculated the energy levels, oscillator strengths, and transition probabilities for eight carbon-like ions (Na vi, Mg vii, Al viii, Si ix, P x, S xi, Cl xii Ar xiii) using Hartree–Fock pseudo-relativistic (HFR) Thomas–Fermi–Dirac–Amaldi (TFDA) approaches. used configuration expansions containing configurations, namely 2s2 2p2, 2s 2p3, 2p 3s, 3p, 3d, 4s, 4p, 5s. For each of con...

For a Bose-Einstein condensate placed in a rotating trap and strongly confined along the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas-Fermi regime for an effective twodimensional ~2D! situation in the x-y plane. We investigate an asymptotic expansion of the energy, the critical angular velocities of nucleation of vortices with respect to a small parameter « ...

This article presents a firm mathematical foundation for the boundary value problem associated with the nonrelativistic Thomas-Fermi equation for heavy atoms in intense magnetic fields. Our approach uses an application of differential inequalities and ideas from nonlinear analysis, including: the technique of lower and upper solutions; and fixed-point theory. We present new results that ensure ...

The Thomas-Fermi method [1] [2] was designed for the calculation of the electron density in a heavy atom, by treating the electrons as locally free. Lieb and Simon [3] showed that the treatment is exact in the limit when the atomic number goes to infinity. Application to a confined Bose condensate was pioneered by Goldman, Silvera, and Legget [4], and by Oliva [5], and recently reconsidered by ...

FOR ATOMS AND HOMONUCLEAR DIATOMIC MOLECULES, IT IS ARGUED THAT THE ELECTRONIC ENERGIES HAVE THE FORMS [FORMULA: see text] and [Formula: see text] [Formula: see text], respectively,where Z is the atomic number, N is the number of electrons, and R is the internuclear distance. By using the Lieb-Simon theorem that the Thomas-Fermi theory is exact in the limit of large atomic number and the Teller...

In the semi-classical limit the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and 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 discussed earlier by Lebowitz and the author. With the help ...