48,544 research outputs found
N electrons in a quantum dot: Two-point Pade approximants
We present analytic estimates for the energy levels of N electrons (N = 2 -
5) in a two-dimensional parabolic quantum dot. A magnetic field is applied
perpendicularly to the confinement plane. The relevant scaled energy is shown
to be a smooth function of the parameter \beta=(effective Rydberg/effective dot
energy)^{1/6}. Two-point Pade approximants are obtained from the series
expansions of the energy near the oscillator () and Wigner
() limits. The approximants are expected to work with an error
not greater than 2.5% in the entire interval .Comment: 27 pages. LaTeX. 6 figures not include
Two and three electrons in a quantum dot: 1/|J| - expansion
We consider systems of two and three electrons in a two-dimensional parabolic
quantum dot. A magnetic field is applied perpendicularly to the electron plane
of motion. We show that the energy levels corresponding to states with high
angular momentum, J, and a low number of vibrational quanta may be
systematically computed as power series in 1/|J|. These states are relevant in
the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure
Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
We extract exact charged black-hole solutions with flat transverse sections
in the framework of D-dimensional Maxwell-f(T) gravity, and we analyze the
singularities and horizons based on both torsion and curvature invariants.
Interestingly enough, we find that in some particular solution subclasses there
appear more singularities in the curvature scalars than in the torsion ones.
This difference disappears in the uncharged case, or in the case where f(T)
gravity becomes the usual linear-in-T teleparallel gravity, that is General
Relativity. Curvature and torsion invariants behave very differently when
matter fields are present, and thus f(R) gravity and f(T) gravity exhibit
different features and cannot be directly re-casted each other.Comment: 24 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1110.402
- …