12 research outputs found
Universal behavior of quantum Green's functions
We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined
in a d-dimensional domain. The object of interest is the time-independent Green
function G_z(r,r') = . Recently, in one dimension (1D),
the Green's function problem was solved explicitly in inverse form, with
diagonal elements of Green's function as prescribed variables. The first aim of
this paper is to extract from the 1D inverse solution such information about
Green's function which cannot be deduced directly from its definition. Among
others, this information involves universal, i.e. u(r)-independent, behavior of
Green's function close to the domain boundary. The second aim is to extend the
inverse formalism to higher dimensions, especially to 3D, and to derive the
universal form of Green's function for various shapes of the confining domain
boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy
The violation of the Hund's rule in semiconductor artificial atoms
The unrestricted Pople-Nesbet approach for real atoms is adapted to quantum
dots, the man-made artificial atoms, under applied magnetic field. Gaussian
basis sets are used instead of the exact single-particle orbitals in the
construction of the appropriated Slater determinants. Both system chemical
potential and charging energy are calculated, as also the expected values for
total and z-component in spin states. We have verified the validity of the
energy shell structure as well as the Hund's rule state population at zero
magnetic field. Above given fields, we have observed a violation of the Hund's
rule by the suppression of triplets and quartets states at the 1p energy shell,
taken as an example. We also compare our present results with those obtained
using the LS-coupling scheme for low electronic occupations. We have focused
our attention to ground-state properties for GaAs quantum dots populated up to
forty electrons.Comment: 5 pages, 2 figures, submitted to Semic. Sci. Techno