2,044 research outputs found
Equivariant Poincar\'e series of filtrations and topology
Earlier, for an action of a finite group on a germ of an analytic
variety, an equivariant -Poincar\'e series of a multi-index filtration in
the ring of germs of functions on the variety was defined as an element of the
Grothendieck ring of -sets with an additional structure. We discuss to which
extend the -Poincar\'e series of a filtration defined by a set of curve or
divisorial valuations on the ring of germs of analytic functions in two
variables determines the (equivariant) topology of the curve or of the set of
divisors
Ab initio calculations of the dynamical response of copper
The role of localized -bands in the dynamical response of Cu is
investigated, on the basis of {\em ab initio} pseudopotential calculations. The
density-response function is evaluated in both the random-phase approximation
(RPA) and a time-dependent local-density functional approximation (TDLDA). Our
results indicate that in addition to providing a polarizable background which
lowers the free-electron plasma frequency, d-electrons are responsible, at
higher energies and small momenta, for a double-peak structure in the dynamical
structure factor. These results are in agreement with the experimentally
determined optical response of copper. We also analyze the dependence of
dynamical scattering cross sections on the momentum transfer.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
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