2,324 research outputs found
Explicit formulas for the generalized Hermite polynomials in superspace
We provide explicit formulas for the orthogonal eigenfunctions of the
supersymmetric extension of the rational Calogero-Moser-Sutherland model with
harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in
superspace. The construction relies on the triangular action of the Hamiltonian
on the supermonomial basis. This translates into determinantal expressions for
the Hamiltonian's eigenfunctions.Comment: 19 pages. This is a recasting of the second part of the first version
of hep-th/0305038 which has been splitted in two articles. In this revised
version, the introduction has been rewritten and a new appendix has been
added. To appear in JP
Jack superpolynomials, superpartition ordering and determinantal formulas
We call superpartitions the indices of the eigenfunctions of the
supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model.
We obtain an ordering on superpartitions from the explicit action of the
model's Hamiltonian on monomial superfunctions. This allows to define Jack
superpolynomials as the unique eigenfunctions of the model that decompose
triangularly, with respect to this ordering, on the basis of monomial
superfunctions. This further leads to a simple and explicit determinantal
expression for the Jack superpolynomials.Comment: 20 pages - minor corrections; to appear in CM
Coherent Transport Through a Quadruple Point in a Few Electron Triple Dot
A few electron double electrostatic lateral quantum dot can be transformed
into a few electron triple quantum dot by applying a different combination of
gate voltages. Quadruple points have been achieved at which all three dots are
simultaneously on resonance. At these special points in the stability diagram
four occupation configurations are possible. Both charge detection and
transport experiments have been performed on this device. In this short paper
we present data and confirm that transport is coherent by observing a Pi phase
shift in magneto-conductance oscillations as one passes through the quadruple
point.Comment: To be published in ICPS Conf. Proceedings 200
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