3,963 research outputs found
The Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters
The nearest neighbor antiferromagnetic Heisenberg model is
considered for spins sitting on the vertices of clusters with the connectivity
of fullerene molecules and a number of sites ranging from 24 to 32. Using
the permutational and spin inversion symmetries of the Hamiltonian the low
energy spectrum is calculated for all the irreducible representations of the
symmetry group of each cluster. Frustration and connectivity result in
non-trivial low energy properties, with the lowest excited states being
singlets except for . Same hexagon and same pentagon correlations are the
most effective in the minimization of the energy, with the
symmetry cluster having an unusually strong singlet intra-pentagon correlation.
The magnetization in a field shows no discontinuities unlike the icosahedral
fullerene clusters, but only plateaux with the most pronounced for
. The spatial symmetry as well as the connectivity of the clusters appear
to be important for the determination of their magnetic properties.Comment: Extended to include low energy spectra, correlation functions and
magnetization data of clusters up to 32 site
Group projector generalization of dirac-heisenberg model
The general form of the operators commuting with the ground representation
(appearing in many physical problems within single particle approximation) of
the group is found. With help of the modified group projector technique, this
result is applied to the system of identical particles with spin independent
interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space
for arbitrary orbital occupation numbers and arbitrary spin. This gives
transparent insight into the physical contents of this hamiltonian, showing
that formal generalizations with spin greater than 1/2 involve nontrivial
additional physical assumptions.Comment: 10 page
Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schr\"odinger Equation with a Kronig-Penney Potential
All Bloch states of the mean field of a Bose-Einstein condensate in the
presence of a one dimensional lattice of impurities are presented in closed
analytic form. The band structure is investigated by analyzing the stationary
states of the nonlinear Schr\"odinger, or Gross-Pitaevskii, equation for both
repulsive and attractive condensates. The appearance of swallowtails in the
bands is examined and interpreted in terms of the condensates superfluid
properties. The nonlinear stability properties of the Bloch states are
described and the stable regions of the bands and swallowtails are mapped out.
We find that the Kronig-Penney potential has the same properties as a
sinusoidal potential; Bose-Einstein condensates are trapped in sinusoidal
optical lattices. The Kronig-Penney potential has the advantage of being
analytically tractable, unlike the sinusoidal potential, and, therefore, serves
as a good model for experimental phenomena.Comment: Version 2. Fixed typos, added referenc
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
Density Functional Theory for the Photoionization Dynamics of Uracil
Photoionization dynamics of the RNA base Uracil is studied in the framework
of Density Functional Theory (DFT). The photoionization calculations take
advantage of a newly developed parallel version of a multicentric approach to
the calculation of the electronic continuum spectrum which uses a set of
B-spline radial basis functions and a Kohn-Sham density functional hamiltonian.
Both valence and core ionizations are considered. Scattering resonances in
selected single-particle ionization channels are classified by the symmetry of
the resonant state and the peak energy position in the photoelectron kinetic
energy scale; the present results highlight once more the site specificity of
core ionization processes. We further suggest that the resonant structures
previously characterized in low-energy electron collision experiments are
partly shifted below threshold by the photoionization processes. A critical
evaluation of the theoretical results providing a guide for future experimental
work on similar biosystems
Noise Can Reduce Disorder in Chaotic Dynamics
We evoke the idea of representation of the chaotic attractor by the set of
unstable periodic orbits and disclose a novel noise-induced ordering
phenomenon. For long unstable periodic orbits forming the strange attractor the
weights (or natural measure) is generally highly inhomogeneous over the set,
either diminishing or enhancing the contribution of these orbits into system
dynamics. We show analytically and numerically a weak noise to reduce this
inhomogeneity and, additionally to obvious perturbing impact, make a
regularizing influence on the chaotic dynamics. This universal effect is rooted
into the nature of deterministic chaos.Comment: 11 pages, 5 figure
Spin Polaron Effective Magnetic Model for La_{0.5}Ca_{0.5}MnO_3
The conventional paradigm of charge order for La_{1-x}Ca_xMnO_3 for x=0.5 has
been challenged recently by a Zener polaron picture emerging from experiments
and theoretical calculations. The effective low energy Hamiltonian for the
magnetic degrees of freedom has been found to be a cubic Heisenberg model, with
ferromagnetic nearest neighbor and frustrating antiferromagnetic next nearest
neighbor interactions in the planes, and antiferromagnetic interaction between
planes. With linear spin wave theory and diagonalization of small clusters up
to 27 sites we find that the behavior of the model interpolates between the A
and CE-type magnetic structures when a frustrating intraplanar interaction is
tuned. The values of the interactions calculated by ab initio methods indicate
a possible non-bipartite picture of polaron ordering differing from the
conventional one.Comment: 21 pages and 8 figures (included), Late
Clebsch-Gordan Construction of Lattice Interpolating Fields for Excited Baryons
Large sets of baryon interpolating field operators are developed for use in
lattice QCD studies of baryons with zero momentum. Operators are classified
according to the double-valued irreducible representations of the octahedral
group. At first, three-quark smeared, local operators are constructed for each
isospin and strangeness and they are classified according to their symmetry
with respect to exchange of Dirac indices. Nonlocal baryon operators are
formulated in a second step as direct products of the spinor structures of
smeared, local operators together with gauge-covariant lattice displacements of
one or more of the smeared quark fields. Linear combinations of direct products
of spinorial and spatial irreducible representations are then formed with
appropriate Clebsch-Gordan coefficients of the octahedral group. The
construction attempts to maintain maximal overlap with the continuum SU(2)
group in order to provide a physically interpretable basis. Nonlocal operators
provide direct couplings to states that have nonzero orbital angular momentum.Comment: This manuscript provides an anlytical construction of operators and
is related to hep-lat/0506029, which provides a computational construction.
This e-print version contains a full set of Clebsch-Gordan coefficients for
the octahedral grou
Fitting Ranked English and Spanish Letter Frequency Distribution in U.S. and Mexican Presidential Speeches
The limited range in its abscissa of ranked letter frequency distributions
causes multiple functions to fit the observed distribution reasonably well. In
order to critically compare various functions, we apply the statistical model
selections on ten functions, using the texts of U.S. and Mexican presidential
speeches in the last 1-2 centuries. Dispite minor switching of ranking order of
certain letters during the temporal evolution for both datasets, the letter
usage is generally stable. The best fitting function, judged by either
least-square-error or by AIC/BIC model selection, is the Cocho/Beta function.
We also use a novel method to discover clusters of letters by their
observed-over-expected frequency ratios.Comment: 7 figure
Numerically improved computational scheme for the optical conductivity tensor in layered systems
The contour integration technique applied to calculate the optical
conductivity tensor at finite temperatures in the case of layered systems
within the framework of the spin-polarized relativistic screened
Korringa-Kohn-Rostoker band structure method is improved from the computational
point of view by applying the Gauss-Konrod quadrature for the integrals along
the different parts of the contour and by designing a cumulative special points
scheme for two-dimensional Brillouin zone integrals corresponding to cubic
systems.Comment: 17 pages, LaTeX + 4 figures (Encapsulated PostScript), submitted to
J. Phys.: Condensed Matter (19 Sept. 2000
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