Hilbert's 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation

Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained

Metal-Insulator Transition and Lattice Instability of Paramagnetic V2O3

We determine the electronic structure and phase stability of paramagnetic V$_2$O$_3$ at the Mott-Hubbard metal-insulator phase transition, by employing a combination of an ab initio method for calculating band structures with dynamical mean-field theory. The structural transformation associated with the metal-insulator transition is found to occur upon a slight expansion of the lattice volume by $\sim 1.5$ %, in agreement with experiment. Our results show that the structural change precedes the metal-insulator transition, implying a complex interplay between electronic and lattice degrees of freedom at the transition. Electronic correlations and full charge self-consistency are found to be crucial for a correct description of the properties of V$_2$O$_3$.Comment: 5 pages, 4 figure

Electronic structure of charge-ordered Fe3O4 from calculated optical, megneto-optical Kerr effect, and O K-edge x-ray absorption spectra

The electronic structure of the low-temperature (LT) monoclinic magnetite, Fe3O4, is investigated using the local spin density approximation (LSDA) and the LSDA+U method. The self-consistent charge ordered LSDA+U solution has a pronounced [001] charge density wave character. In addition, a minor [00{1/2}] modulation in the phase of the charge order (CO) also occurs. While the existence of CO is evidenced by the large difference between the occupancies of the minority spin t_{2g} states of ``2+'' and ``3+'' Fe_B cations, the total 3d charge disproportion is small, in accord with the valence-bond-sum analysis of structural data. Weak Fe orbital moments of ~0.07 mB are obtained from relativistic calculations for the CO phase which is in good agreement with recent x-ray magnetic circular dichroism measurements. Optical, magneto-optical Kerr effect, and O K-edge x-ray absorption spectra calculated for the charge ordered LSDA+U solution are compared to corresponding LSDA spectra and to available experimental data. Reasonably good agreement between the theoretical and experimental spectra supports the relevance of the CO solution obtained for the monoclinic LT phase. The results of calculations of effective exchange coupling constants between Fe spin magnetic moments are also presented.Comment: 32 pages, 10 figure

Correlation strength, Lifshitz transition and the emergence of a two- to three-dimensional crossover in FeSe under pressure

We report a detailed theoretical study of the electronic structure, spectral properties, and lattice parameters of bulk FeSe under pressure using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory method (DFT+DMFT). In particular, we perform a structural optimization and compute the evolution of the lattice parameters (volume, $c/a$ ratio, and the internal $z$ position of Se) and the electronic structure of the tetragonal (space group $P4/nmm$) paramagnetic FeSe. Our results for the lattice parameters are in good quantitative agreement with experiment. The $c/a$ ratio is slightly overestimated by about $3$~\%, presumably due to the absence of the van der Waals interactions between the FeSe layers in our calculations. The lattice parameters determined within DFT are off the experimental values by a remarkable $\sim$$6$-$15$~\%, implying a crucial importance of electron correlations. Upon compression to $10$~GPa, the $c/a$ ratio and the lattice volume show a decrease by $2$ and $10$~\%, respectively, while the Se $z$ coordinate weakly increases by $\sim$$2$~\%. Most importantly, our results reveal a topological change of the Fermi surface (Lifshitz transition) which is accompanied by a two- to three-dimensional crossover. Our results indicate a small reduction of the quasiparticle mass renormalization $m^*/m$ by about $5$~\% for the $e$ and less than $1$~\% for the $t_2$ states, as compared to ambient pressure. The behavior of the momentum-resolved magnetic susceptibility $\chi({\bf q})$ shows no topological changes of magnetic correlations under pressure, but demonstrates a reduction of the degree of the in-plane $(\pi,\pi)$ stripe-type nesting. Our results for the electronic structure and lattice parameters of FeSe are in good qualitative agreement with recent experiments on its isoelectronic counterpart FeSe$_{1-x}$S$_x$.Comment: 10 pages, 6 figure

Charge order and spin-singlet pairs formation in Ti4O7

Charge ordering in the low-temperature triclinic structure of titanium oxide (Ti4O7) is investigated using the local density approximation (LDA)+U method. Although the total 3d charge separation is rather small, an orbital order parameter defined as the difference between t2g occupancies of Ti$^{3+}$ and Ti$^{4+}$ cations is large and gives direct evidence for charge ordering. Ti 4s and 4p states make a large contribution to the static "screening" of the total 3d charge difference. This effective charge screening leads to complete loss of the disproportionation between the charges at 3+ and 4+ Ti sites. The occupied t2g states of Ti$^{3+}$ cations are predominantly of $d_{xy}$ character and form a spin-singlet molecular orbital via strong direct antiferromagnetic exchange coupling between neighboring Ti(1) and Ti(3) sites, whereas the role of superexchange is found to be negligible.Comment: 6 pages, 4 figure

Charge order in Fe2OBO3: An LSDA+U study

Charge ordering in the low-temperature monoclinic structure of iron oxoborate (Fe2OBO3) is investigated using the local spin density approximation (LSDA)+U method. While the difference between t_{2g} minority occupancies of Fe^{2+} and Fe^{3+} cations is large and gives direct evidence for charge ordering, the static "screening" is so effective that the total 3d charge separation is rather small. The occupied Fe^{2+} and Fe^{3+} cations are ordered alternately within the chain which is infinite along the a-direction. The charge order obtained by LSDA+U is consistent with observed enlargement of the \beta angle. An analysis of the exchange interaction parameters demonstrates the predominance of the interribbon exchange interactions which determine the whole L-type ferrimagnetic spin structure.Comment: 7 pages, 8 figure

Calculated phonon spectra of paramagnetic iron at the alpha-gamma phase transition

We compute lattice dynamical properties of iron at the bcc-fcc phase transition using dynamical mean-field theory implemented with the frozen-phonon method. Electronic correlations are found to have a strong effect on the lattice stability of paramagnetic iron in the bcc phase. Our results for the structural phase stability and lattice dynamical properties of iron are in good agreement with experiment.Comment: 4 pages, 2 figure

Comparative Characteristics of Time Perspective of Professional Athletes and Drug Addicted People

AbstractThe present article analyses the comparative characteristics of time perspective of professional athletes and drug addicted people. Participants who are addicted to drugs and professional athletes pose significant difference in time perspective: in their perception of “Future”, “Negative Past” and Positive Past”. Characteristics of time perspective are dynamic and change in the context of meaning-life orientations and stressful events. Excessive concentration of participants on the past or on the future could be a predictor that contributes to dependent behavior. The necessity of individual profile consideration in psychological work with athletes and drug-addicted people was shown