1,958 research outputs found
Conditions for Optimality and Strong Stability in Nonlinear Programs without assuming Twice Differentiability of Data
The present paper is concerned with optimization problems in which the data are differentiable functions having a continuous or locally Lipschitzian gradient mapping. Its main purpose is to develop second-order sufficient conditions for a stationary solution to a program with C^{1,1} data to be a strict local minimizer or to be a local minimizer which is even strongly stable with respect to certain perturbations of the data. It turns out that some concept of a set-valued directional derivative of a Lipschitzian mapping is a suitable tool to extend well-known results in the case of programs with twice differentiable data to more general situations. The local minimizers being under consideration have to satisfy the Mangasarian-Fromovitz CQ. An application to iterated local minimization is sketched
Paramagnon dispersion in -FeSe observed by Fe -edge resonant inelastic x-ray scattering
We report an Fe -edge resonant inelastic x-ray scattering (RIXS) study of
the unusual superconductor -FeSe. The high energy resolution of this
RIXS experiment (55meV FWHM) made it possible to resolve
low-energy excitations of the Fe manifold. These include a broad peak
which shows dispersive trends between 100-200meV along the and
directions of the one-Fe square reciprocal lattice, and which can
be attributed to paramagnon excitations. The multi-band valence state of FeSe
is among the most metallic in which such excitations have been discerned by
soft x-ray RIXS
Similar temperature scale for valence changes in Kondo lattices with different Kondo temperatures
The Kondo model predicts that both the valence at low temperatures and its
temperature dependence scale with the characteristic energy T_K of the Kondo
interaction. Here, we study the evolution of the 4f occupancy with temperature
in a series of Yb Kondo lattices using resonant X-ray emission spectroscopy. In
agreement with simple theoretical models, we observe a scaling between the
valence at low temperature and T_K obtained from thermodynamic measurements. In
contrast, the temperature scale T_v at which the valence increases with
temperature is almost the same in all investigated materials while the Kondo
temperatures differ by almost four orders of magnitude. This observation is in
remarkable contradiction to both naive expectation and precise theoretical
predictions of the Kondo model, asking for further theoretical work in order to
explain our findings. Our data exclude the presence of a quantum critical
valence transition in YbRh2Si2
High-resolution resonant inelastic soft X-ray scattering as a probe of the crystal electrical field in lanthanides demonstrated for the case of CeRh2Si2
The magnetic properties of rare earth compounds are usually well captured by
assuming a fully localized f shell and only considering the Hund's rule ground
state multiplet split by a crystal electrical field (CEF). Currently, the
standard technique for probing CEF excitations in lanthanides is inelastic
neutron scattering. Here we show that with the recent leap in energy
resolution, resonant inelastic soft X-ray scattering has become a serious
alternative for looking at CEF excitations with some distinct advantages
compared to INS. As an example we study the CEF scheme in CeRh2Si2, a system
that has been intensely studied for more than two decades now but for which no
consensus has been reached yet as to its CEF scheme. We used two new features
that have only become available very recently in RIXS, high energy resolution
of about 30 meV as well as polarization analysis in the scattered beam, to find
a unique CEF description for CeRh2Si2. The result agrees well with previous INS
and magnetic susceptibility measurements. Due to its strong resonant character,
RIXS is applicable to very small samples, presents very high cross sections for
all lanthanides, and further benefits from the very weak coupling to phonon
excitation. The rapid progress in energy resolution of RIXS spectrometers is
making this technique increasingly attractive for the investigation of the CEF
scheme in lanthanides
- …