6,452 research outputs found
Systematic generation of finite-range atomic basis sets for linear-scaling calculations
Basis sets of atomic orbitals are very efficient for density functional
calculations but lack a systematic variational convergence.
We present a variational method to optimize numerical atomic orbitals using a
single parameter to control their range.
The efficiency of the basis generation scheme is tested and compared with
other schemes for multiple zeta basis sets.
The scheme shows to be comparable in quality to other widely used schemes
albeit offering better performance for linear-scaling computations
The restriction of the Ising model to a layer
We discuss the status of recent Gibbsian descriptions of the restriction
(projection) of the Ising phases to a layer. We concentrate on the projection
of the two-dimensional low temperature Ising phases for which we prove a
variational principle.Comment: 38 page
Variational Principle underlying Scale Invariant Social Systems
MaxEnt's variational principle, in conjunction with Shannon's logarithmic
information measure, yields only exponential functional forms in
straightforward fashion. In this communication we show how to overcome this
limitation via the incorporation, into the variational process, of suitable
dynamical information. As a consequence, we are able to formulate a somewhat
generalized Shannonian Maximum Entropy approach which provides a unifying
"thermodynamic-like" explanation for the scale-invariant phenomena observed in
social contexts, as city-population distributions. We confirm the MaxEnt
predictions by means of numerical experiments with random walkers, and compare
them with some empirical data
Atiyah-Manton Approach to Skyrmion Matter
We propose how to approach, and report on the first results in our effort
for, describing nuclear matter starting from the solitonic picture of baryons
which is supposed to represent QCD for large number of colors. For this
purpose, the instanton-skyrmion connection of Atiyah and Manton is exploited to
describe skyrmion matter. We first modify 't Hooft's multi-instanton solution
so as to suitably incorporate proper dynamical variables into the skyrmion
matter and then by taking these variables as variational parameters, we show
that they cover a configuration space sufficient to adequately describe the
ground state properties of nuclear matter starting from the skyrmion picture.
Our results turn out to be comparable to those so far found in different
numerical calculations, with our solution reaching stability at high density
for a crystal structure and obtaining a comparable value for the energy per
baryon at the minimum, thus setting the stage for the next step
Impurity crystal in a Bose-Einstein condensate
We investigate the behavior of impurity fields immersed in a larger
condensate field in 1, 2, and 3 dimensions. We discuss the localization of a
single impurity field within a condensate and note the effects of surface
energy. We derive the functional form of the attractive interaction between two
impurities due to mediation from the condensate. Generalizing the analysis to
impurity fields, we show that within various parameter regimes a crystal of
impurity fields can form spontaneously in the condensate. Finally, the system
of condensate and crystallized impurity structure is shown to have nonclassical
rotational inertia, which is characteristic of superfluidity, i.e. the system
can be seen to exhibit supersolid behavior.Comment: 5 pages, 3 color figures; Accepted to Phys. Rev. Let
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