6,609 research outputs found
Convergence of density-matrix expansions for nuclear interactions
We extend density-matrix expansions in nuclei to higher orders in derivatives
of densities and test their convergence properties. The expansions allow for
converting the interaction energies characteristic to finite- and short-range
nuclear effective forces into quasi-local density functionals. We also propose
a new type of expansion that has excellent convergence properties when
benchmarked against the binding energies obtained for the Gogny interaction.Comment: 4 pages, 3 figure
Order-N Density-Matrix Electronic-Structure Method for General Potentials
A new order-N method for calculating the electronic structure of general
(non-tight-binding) potentials is presented. The method uses a combination of
the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and
Daw, and a representation of the density matrix based on ``travelling basis
orbitals''. The method is applied to several one-dimensional examples,
including the free electron gas, the ``Morse'' bound-state potential, a
discontinuous potential that mimics an interface, and an oscillatory potential
that mimics a semiconductor. The method is found to contain Friedel
oscillations, quantization of charge in bound states, and band gap formation.
Quantitatively accurate agreement with exact results is found in most cases.
Possible advantages with regard to treating electron-electron interactions and
arbitrary boundary conditions are discussed.Comment: 13 pages, REVTEX, 7 postscript figures (not quite perfect
Correlation studies of fission fragment neutron multiplicities
We calculate neutron multiplicities from fission fragments with specified
mass numbers for events having a specified total fragment kinetic energy. The
shape evolution from the initial compound nucleus to the scission
configurations is obtained with the Metropolis walk method on the
five-dimensional potential-energy landscape, calculated with the
macroscopic-microscopic method for the three-quadratic-surface shape family.
Shape-dependent microscopic level densities are used to guide the random walk,
to partition the intrinsic excitation energy between the two proto-fragments at
scission, and to determine the spectrum of the neutrons evaporated from the
fragments. The contributions to the total excitation energy of the resulting
fragments from statistical excitation and shape distortion at scission is
studied. Good agreement is obtained with available experimental data on neutron
multiplicities in correlation with fission fragments from U(n,f). At higher neutron energies a superlong fission mode appears which
affects the dependence of the observables on the total fragment kinetic energy.Comment: 12 pages, 10 figure
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and generalize readily to multidimensional
persistence modules. In this paper, we develop the theory of multidimensional
interleavings, with a view towards applications to topological data analysis.
We present four main results. First, we show that on 1-D persistence modules,
is equal to the bottleneck distance . This result, which first
appeared in an earlier preprint of this paper, has since appeared in several
other places, and is now known as the isometry theorem. Second, we present a
characterization of the -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that restricts to a metric on isomorphism
classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in
Foundations of Computational Mathematics. 36 page
Effects of three-nucleon forces and two-body currents on Gamow-Teller strengths
We optimize chiral interactions at next-to-next-to leading order to
observables in two- and three-nucleon systems, and compute Gamow-Teller
transitions in carbon-14, oxygen-22 and oxygen-24 using consistent two-body
currents. We compute spectra of the daughter nuclei nitrogen-14, fluorine-22
and fluorine-24 via an isospin-breaking coupled-cluster technique, with several
predictions. The two-body currents reduce the Ikeda sum rule, corresponding to
a quenching factor q^2 ~ 0.84-0.92 of the axial-vector coupling. The half life
of carbon-14 depends on the energy of the first excited 1+ state, the
three-nucleon force, and the two-body current
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