10,983 research outputs found
Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking
We address low-density two-dimensional circular quantum dots with
spin-restricted Kohn-Sham density functional theory. By using an
exchange-correlation functional that encodes the effects of the
strongly-correlated regime (and that becomes exact in the limit of infinite
correlation), we are able to reproduce characteristic phenomena such as the
formation of ring structures in the electronic total density, preserving the
fundamental circular symmetry of the system. The observation of this and other
well-known effects in Wigner-localized quantum dots such as the flattening of
the addition energy spectra, has until now only been within the scope of other,
numerically more demanding theoretical approachesComment: 8 pages, 6 figure
Vertex adjacencies in the set covering polyhedron
We describe the adjacency of vertices of the (unbounded version of the) set
covering polyhedron, in a similar way to the description given by Chvatal for
the stable set polytope. We find a sufficient condition for adjacency, and
characterize it with similar conditions in the case where the underlying matrix
is row circular. We apply our findings to show a new infinite family of
minimally nonideal matrices.Comment: Minor revision, 22 pages, 3 figure
On totally geodesic submanifolds in the Jacobian locus
We study submanifolds of A_g that are totally geodesic for the locally
symmetric metric and which are contained in the closure of the Jacobian locus
but not in its boundary. In the first section we recall a formula for the
second fundamental form of the period map due to Pirola, Tortora and the first
author. We show that this result can be stated quite neatly using a line bundle
over the product of the curve with itself. We give an upper bound for the
dimension of a germ of a totally geodesic submanifold passing through [C] in
M_g in terms of the gonality of C. This yields an upper bound for the dimension
of a germ of a totally geodesic submanifold contained in the Jacobian locus,
which only depends on the genus. We also study the submanifolds of A_g obtained
from cyclic covers of the projective line. These have been studied by various
authors. Moonen determined which of them are Shimura varieties using deep
results in positive characteristic. Using our methods we show that many of the
submanifolds which are not Shimura varieties are not even totally geodesic.Comment: To appear on International Journal of Mathematic
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