577 research outputs found
Fast and Robust Algorithm for the Energy Minimization of Spin Systems Applied in an Analysis of High Temperature Spin Configurations in Terms of Skyrmion Density
An algorithm for the minimization of the energy of magnetic systems is
presented and applied to the analysis of thermal configurations of a
ferromagnet to identify inherent structures, i.e. the nearest local energy
minima, as a function of temperature. Over a rather narrow temperature
interval, skyrmions appear and reach a high temperature limit for the skyrmion
density. In addition, the performance of the algorithm is further demonstrated
in a self-consistent field calculation of a skyrmion in an itinerant magnet.
The algorithm is based on a geometric approach in which the curvature of the
spherical domain is taken into account and as a result the length of the
magnetic moments is preserved in every iteration. In the limit of infinitesimal
rotations, the minimization path coincides with that obtained using damped spin
dynamics while the use of limited-memory quasi-newton minimization algorithms,
such as the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm,
significantly accelerates the convergence
Variational density functional calculations of excited states via direct optimization
The development of variational density functional theory approaches to
excited electronic states is impeded by limitations of the commonly used
self-consistent field (SCF) procedure. A method based on a direct optimization
approach as well as the maximum overlap method is presented and the performance
compared with previously proposed SCF strategies. Excited-state solutions
correspond to saddle points of the energy as a function of the electronic
degrees of freedom. The approach presented here makes use of a preconditioner
determined with the help of the maximum overlap method to guide the convergence
on a target nth-order saddle point. The method is found to be more robust and
to converge faster than previously proposed SCF approaches for a set of 89
excited states of molecules. A limited-memory formulation of the symmetric
rank-one method for updating the inverse Hessian is found to give the best
performance. A conical intersection for the carbon monoxide molecule is
calculated without resorting to fractional occupation numbers. Calculations on
excited states of the hydrogen atom and a doubly excited state of the
dihydrogen molecule using a self-interaction corrected functional are
presented. For these systems, the self-interaction correction is found to
improve the accuracy of density functional calculations of excited states
Direct Optimization Method for Variational Excited-State Density Functional Calculations Using Real Space Grid or Plane Waves
A direct optimization method is presented for density functional calculations
of excited electronic states using either a real space grid or a plane wave
basis set. The method is variational, provides atomic forces in the excited
states, and can be applied to Kohn-Sham (KS) functionals as well as
orbital-density dependent functionals (ODD) including explicit self-interaction
correction. The implementation for KS functionals involves two nested loops:
(1) An inner loop for finding a stationary point in a subspace spanned by the
occupied and a few virtual orbitals corresponding to the excited state; (2) an
outer loop for minimizing the energy in a tangential direction. For ODD
functionals, a third loop is used to find the unitary transformation that
minimizes the energy functional among occupied orbitals only. Combined with the
maximum overlap method, the algorithm converges in challenging cases where
conventional self-consistent field algorithms tend to fail. The benchmark tests
presented include two charge-transfer excitations in nitrobenzene and an
excitation of CO to degenerate orbitals where the importance of
complex orbitals is illustrated. An application of the method to several
metal-to-ligand charge-transfer and metal-centred excited states of an Fe photosensitizer complex is described and the results compared to reported
experimental estimates. The method is also used to study the effect of
Perdew-Zunger self-interaction correction on valence and Rydberg excited states
of several molecules, both singlet and triplet states. The correction is found
to improve the description of molecular bond stretching but calculated values
of the excitation energy are improved only slightly, by {\it ca.} 0.1 eV, due
to cancellation of the estimated self-interaction error in the ground and
excited states.Comment: 55 pages, 12 figures, including supporting Informatio
Direct Energy Minimization Based on Exponential Transformation in Density Functional Calculations of Finite and Extended Systems
The energy minimization involved in density functional calculations of
electronic systems can be carried out using an exponential transformation that
preserves the orthonormality of the orbitals. The energy of the system is then
represented as a function of the elements of a skew-Hermitian matrix that can
be optimized directly using unconstrained minimization methods. An
implementation based on the limited memory Broyden-Fletcher-Goldfarb-Shanno
approach with inexact line search and a preconditioner is presented and the
performance compared with that of the commonly used self-consistent field
approach. Results are presented for the G2 set of 148 molecules, liquid water
configurations with up to 576 molecules and some insulating crystals. A general
preconditioner is presented that is applicable to systems with fractional
orbital occupation as is, for example, needed in the k-point sampling for
periodic systems. This exponential transformation direct minimization approach
is found to outperform the standard implementation of the self-consistent field
approach in that all the calculations converge with the same set of parameter
values and it requires less computational effort on average. The formulation of
the exponential transformation and the gradients of the energy presented here
are quite general and can be applied to energy functionals that are not unitary
invariant such as self-interaction corrected functionals
Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations
In this perspective, the various measures of electron correlation used in
wavefunction theory, density functional theory and quantum information theory
are briefly reviewed. We then focus on a more traditional metric based on
dominant weights in the full configuration solution and discuss its behaviour
with respect to the choice of the -electron and the one-electron basis. The
impact of symmetry is discussed and we emphasize that the distinction between
determinants, configuration state functions and configurations as reference
functions is useful because the latter incorporate spin-coupling into the
reference and should thus reduce the complexity of the wavefunction expansion.
The corresponding notions of single determinant, single spin-coupling and
single configuration wavefunctions are discussed and the effect of orbital
rotations on the multireference character is reviewed by analysing a simple
model system. In molecular systems, the extent of correlation effects should be
limited by finite system size and in most cases the appropriate choices of
one-electron and -electron bases should be able to incorporate these into a
low-complexity reference function, often a single configurational one
New Cases of Scalping from the Burial Grounds of the Pre-Caucasus and the North Caucasus in the Early Iron Age
Several skulls dated to the Early Iron Age discovered in various burial grounds located in the Prikuban and North Caucasus regions are examined in the article. All the skulls are dated to the early Iron Age. The skulls exhibit distinctive signs of scalping. Two of the skulls originate from the Meotian burial ground found in the Starokorsunsky hillfort No. 2, situated near Krasnodar and spanning from the 6th century BC to the 3rd century AD. One of the skulls was excavated from an ancient rural settlement dating to the 2nd centuries BC near the village of Starotitarovskaya in the Krasnodar region. Finally, the remaining skull was unearthed at the Gaston Uota site in Digor Gorge, North Ossetia. This site, concerning the Kobani culture, is dated between the 7th century BC and the 1st half of 4th century BC. The article presents four new instances of scalping originating from Southern Russia. All of the skulls belonged to adult males, and two of them exhibited injuries that appear to have occurred shortly before death. Among the skulls found at the Gaston-Uota burial ground and the settlement near Starotitarovskaya, scalping was executed in the conventional manner, entailing full-scale incisions over the entire hair-covered area. On the other hand, victims buried at the Starokorsunsky hillfort No. 2 displayed evidence of partial scalping, where only the top portion of the cranium vault was scalped, resulting in a limited area of scalp removal. This discrepancy in scalping techniques may reflect distinct cultural traditions associated with this ritualistic practice
A System for Measurement of Convection Aboard Space Station
A simple device for direct measurement of buoyancy driven fluid flows in a low-gravity environment is proposed. A system connecting spacecraft accelerometers data and results of thermal convection in enclosure measurements and numerical simulations is developed. This system will permit also to evaluate the low frequency microacceleration component. The goal of the paper is to present objectives and current results of ground-based experimental and numerical modeling of this convection detector
Robust cryogenic matched low-pass coaxial filters for quantum computing applications
Electromagnetic noise is one of the key external factors decreasing
superconducting qubits coherence. Matched coaxial filters can prevent microwave
and IR photons negative influence on superconducting quantum circuits. Here, we
report on design and fabrication route of matched low-pass coaxial filters for
noise-sensitive measurements at milliKelvin temperatures. A robust transmission
coefficient with designed linear absorption (-1dB/GHz) and ultralow reflection
losses less than -20 dB up to 20 GHz is achieved. We present a mathematical
model for evaluating and predicting filters transmission parameters depending
on their dimensions. It is experimentally approved on two filters prototypes
different lengths with compound of Cu powder and Stycast commercial resin
demonstrating excellent matching. The presented design and assembly route are
universal for various compounds and provide high repeatability of geometrical
and microwave characteristics. Finally, we demonstrate three filters with
almost equal reflection and transmission characteristics in the range from 0 to
20 GHz, which is quite useful to control multiple channel superconducting
quantum circuits.Comment: 5 pages, 4 figure
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