Exact local density method for linear harmonic oscillator

Lawes, G. P.; March, N. H.

doi:10.1063/1.438398

Cited by 63 publications

(63 citation statements)

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“…Given this wider relevance of the model, harmonic confinement is probably the simplest way to realize an inhomogeneous quantum fluid on which to test the ideas and the implementations of Density Functional Theory [6]. Of specific interest in the present context is the kinetic energy functional, which can be constructed exactly from the particle density in the case of N fermions moving independently in a harmonic oscillator potential [7]. Finally, the shell structure that was noticed in the particle density of the Fermi gas in 3D [8] is greatly enhanced in lower dimensionality [9,10].…”

Section: Introductionmentioning

confidence: 99%

Light scattering from a degenerate quasi-one-dimensional confined gas of noninteracting fermions

Vignolo¹,

Minguzzi²,

Tosi³

2001

Phys. Rev. A

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We evaluate the scattering functions of a gas of spin-polarized, non-interacting fermions confined in a quasi-onedimensional harmonic trap at zero temperature. The main focus is on the inelastic scattering spectrum and on the angular distribution of scattered light from a mesoscopic atomic cloud as probes of its discrete quantum levels and of its shell structure in this restricted geometry. The dynamic structure factor is calculated and compared with the results of a local-density approximation exploiting the spectrum of a one-dimensional homogeneous Fermi gas. The elastic and inelastic contributions to the static structure factor are separately evaluated: the inelastic term becomes dominant as the momentum transfer increases, masking a small peak at twice the Fermi momentum in the elastic term but still reflecting the discrete quantum levels of the cloud. A fast and accurate numerical method is developed to evaluate the full pair distribution function for mesoscopic inhomogeneous clouds.

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Section: Introductionmentioning

confidence: 99%

Light scattering from a degenerate quasi-one-dimensional confined gas of noninteracting fermions

Vignolo¹,

Minguzzi²,

Tosi³

2001

Phys. Rev. A

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“…However, for this particular model the expression for single-particle kinetic energy is known for an arbitrary number of levels [12, 131, with and, as we demonstrated previously, this equation contains as limit both the Weizsäcker form for N = 1 and the Thomas-Fermi limit as N oo [12]. Of course, the above relations hold only for a particular harmonic oscillator model which is known to be local [14]. For the general atomic or molecular case, the similar relations are more complicated and nonlocal.…”

Section: ( X )mentioning

confidence: 99%

On the Single-Particle Kinetic Energy Density Functional in Hyper-spherical Reprezentation

Kozlowski

1991

Acta Phys. Pol. A

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The properties of hyperspherical representation where the one-body orbitals are expressed in terms of the square root of the electron density, p(r) and the angle functions {θi(r)}i=1 . N-1 , (R.F. Nalewajski, P.M. Kozlowski, Acta Phys. Pol. Α74, 287 (1988)) are discussed, and the expression for the kinetic energy density functional is analyzed. This expression contains the Weizsäcker term plus a correction determined by the angle functions: Taking into account both the limit of only one occupied level and the slowly varying electron density with large N, it is shown that the kinetic energy density functional interpolates correctly between the known results. Finally, an example of a linear harmonic oscillator is given and the relation between the usual orbital pictures is discussed.PACS numbers: 02.90.+ρ, 31.20.Sy Density Functional Theory (DFT) has some advantages in the theory of many body systems such as atoms, molecules and the solid state. One of the most important problems in DFT is to derive the single-particle kinetic energy density functional Ts [p(r)] in terms of the electron density p(r) and its lowest derivatives. The simplest and most basic formulation of DFT is embodied in Thomas-Fermi (TF) theory, since the kinetic energy is approximated by that corresponding to a free electron gas e.g. a homogeneous system [1]. Construction of an adequate kinetic energy density functional is closely related to the problem of N-representability, namely, for a given density p(r) with p(r) ≥ 0 and f p(r)dr = N, is it always possible to find antisymmetric, N-electron wave function leading to this density? The usual approach is based on construction of a set of orthonormal functions which are continuous, smooth, and extended over all space. This approach has been discussed in the literature by many authors, for example Macke [2], Gilbert (655)

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“…Equation (16) achieves that aim quite explicitly for closed shells in the harmonic potential (1). It is the three-dimensional generalization of the early result of Lawes and March [5] for one-dimensional harmonic confinement.…”

Section: Density Functional Theorymentioning

confidence: 99%

“…Again, we can make a useful analogy with the onedimensional harmonic oscillator. With N singly occupied shells we can write, following Lawes and March [5]:…”

Section: Turning Points Of Particle and Kinetic Energy Densitiesmentioning

confidence: 99%