19,338 research outputs found
Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface
Aramayona and Leininger have provided a "finite rigid subset"
of the curve complex of a surface
, characterized by the fact that any simplicial injection
is induced by a unique element
of the mapping class group . In this paper we prove that,
in the case of the sphere with marked points, the reduced homology
class of the finite rigid set of Aramayona and Leininger is a
-module generator for the reduced homology of the curve
complex , answering in the affirmative a question posed by
Aramayona and Leininger. For the surface with
and we find that the finite rigid set of
Aramayona and Leininger contains a proper subcomplex whose reduced
homology class is a -module generator for the reduced
homology of but which is not itself rigid.Comment: 21 pages, 7 figures; Section 4 revised along with minor corrections
throughou
Kohn-Sham calculations combined with an average pair-density functional theory
A recently developed formalism in which Kohn-Sham calculations are combined
with an ``average pair density functional theory'' is reviewed, and some new
properties of the effective electron-electron interaction entering in this
formalism are derived. A preliminary construction of a fully self-consitent
scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th
International Workshop on Condensed Matter Theories
Comments on alternative calculations of the broadening of spectral lines of neutral sodium by H-atom collisions
With the exception of the sodium D-lines recent calculations of line
broadening cross-sections for several multiplets of sodium by Leininger et al
(2000) are in substantial disagreement with cross-sections interpolated from
the tables of Anstee and O'Mara (1995) and Barklem and O'Mara (1997). The
discrepancy is as large as a factor of three for the 3p-4d multiplet. The two
theories are tested by using the results of each to synthesize lines in the
solar spectrum. It is found that generally the data from the theory of Anstee,
Barklem and O'Mara produce the best match to the observed solar spectrum. It is
found, using a simple model for reflection of the optical electron by the
potential barrier between the two atoms, that the reflection coefficient is too
large for avoided crossings with the upper states of subordinate lines to
contribute to line broadening, supporting the neglect of avoided ionic
crossings by Anstee, Barklem and O'Mara for these lines. The large
discrepancies between the two sets of calculations is a result of an
approximate treatment of avoided ionic crossings for these lines by Leininger
et al (2000).Comment: 18 pages, 5 ps figures included, to appear in J Phys B: At. Mol. Opt.
Phy
Long-range-corrected hybrids including RPA correlation
We recently demonstrated a connection between the random phase approximation
(RPA) and coupled cluster theory [J. Chem. Phys. 129, 231101 (2008)]. Based on
this result, we here propose and test a simple scheme for introducing
long-range RPA correlation into density functional theory. Our method provides
good thermochemical results and models van derWaals interactions accurately.Comment: Accepted version of the manuscrip
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