28,308 research outputs found
The Mayer series of the Lennard-Jones gas: improved bounds for the convergence radius
We provide a lower bound for the convergence radius of the Mayer series of
the Lennard-Jones gas which strongly improves on the classical bound obtained
by Penrose and Ruelle 1963. To obtain this result we use an alternative
estimate recently proposed by Morais et al. (J. Stat. Phys. 2014) for a
restricted class of stable and tempered pair potentials (namely those which can
be written as the sum of a non-negative potential plus an absolutely integrable
and stable potential) combined with a method developed by Locatelli and Schoen
(J. Glob. Optim. 2002) for establishing a lower bound for the minimal
interatomic distance between particles interacting via a Morse potential in a
cluster of minimum-energy configurations
Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
By shifting the reference system for the local-density approximation (LDA)
from the electron gas to other model systems one obtains a new class of density
functionals, which by design account for the correlations present in the chosen
reference system. This strategy is illustrated by constructing an explicit LDA
for the one-dimensional Hubbard model. While the traditional {\it ab initio}
LDA is based on a Fermi liquid (the electron gas), this one is based on a
Luttinger liquid. First applications to inhomogeneous Hubbard models, including
one containing a localized impurity, are reported.Comment: 4 pages, 4 figures (final version, contains additional applications
and discussion; accepted by Phys. Rev. Lett.
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