Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the 2D Hubbard model

Comparing experimental data for high temperature cuprate superconductors with numerical results for electronic models, it is becoming apparent that a hopping along the plaquette diagonals has to be included to obtain a quantitative agreement. According to recent estimations the value of the diagonal hopping $t'$ appears to be material dependent. However, the values for $t'$ discussed in the literature were obtained comparing theoretical results in the weak coupling limit with experimental photoemission data and band structure calculations. The goal of this paper is to study how $t'$ gets renormalized as the interaction between electrons, $U$, increases. For this purpose, the effect of adding a bare diagonal hopping $t'$ to the fully interacting two dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Positive and negative values of $t'$ are analyzed. Spin-spin correlations, $n(\bf{k})$, $\langle n\rangle$ vs $\mu$, and local magnetic moments are studied for values of $U/t$ ranging from 0 to 6, and as a function of the electronic density. The influence of the diagonal hopping in the spectral function $A(\bf{k},\omega)$ is also discussed, and the changes in the gap present in the density of states at half-filling are studied. We introduce a new criterion to determine probable locations of Fermi surfaces at zero temperature from $n(\bf{k})$ data obtained at finite temperature. It appears that hole pockets at ${\bf{k}}=(\pi/2,\pi/2)$ may be induced for negative $t'$ while a positive $t'$ produces similar features at ${\bf{k}}=(\pi,0)$ and $(0,\pi)$. Comparisons with the standard 2D Hubbard ($t'=0$) model indicate that a negative $t'$ hopping amplitude appears to be dynamically generated. In general, we conclude that it is very dangerous to extract a bare parameter of the Hamiltonian $(t')$ from PES data whereComment: 9 pages (RevTex 3.0), 12 figures (postscript), files packed with uufile

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

Bistabilities in twisted nematics with a holding voltage

We study the bistability between a 180° twisted state and its topologically equivalent planar vertical state in pure nematics in the presence of a holding voltage. These bistable states can be distinguished optically by incorporating a pleochroic dye guest into the liquid crystal host. The holding voltage range ΔV of the bistability is found to increase with decreasing k1/k 3 and with decreasing dielectric anisotropy. With reasonable elastic constants and dielectric anisotropy parameter (ε∥ — ε ⊥)/ε⊥ = 0.05, the theoretical holding voltage range ΔV is about 7 % in the idealized case of perfect alignment and zero boundary tilt bias. With such boundary conditions, the cell would be subject to oppositely tilted and oppositely twisted domains, whose elimination would entail a drastic reduction of ΔV and some loss of contrast. While the bistability could probably be demonstrated experimentally, it is not likely to be practical in displays without major materials innovation to obtain significantly lower values of the elastic constant ratio k1/k3.On étudie la bistabilité entre un état en hélice à 180° et l'état planaire vertical topologiquement équivalent dans les nématiques purs soumis à une tension. On peut distinguer optiquement ces états bistables en mélangeant un colorant pléochroïque avec le cristal liquide. L'intervalle de tension ΔV pour lequel on observe la bistabilité s'accroit à mesure que décroissent le rapport k1/k3 et la valeur du paramètre d'anisotropie diélectrique. Avec des constantes élastiques plausibles et avec un paramètre d'anisotropie diélectrique (ε ∥ — ε⊥)/ε ⊥ = 0,05, l'intervalle théorique de tension ΔV où la bistabilité existe est à peu près 7 % dans le cas idéal où l'alignement est à 180° et où le directeur est parallèle à la surface. Avec de telles conditions aux limites, la cellule serait sujette à des domaines en hélice, de sens inverse ainsi qu'à des domaines inclinés en sens inverse, dont l'élimination entraînerait une réduction importante de l'intervalle ΔV et une diminution de contraste. Bien que la bistabilité puisse être démontrée expérimentalement, il n'est pas probable qu'elle soit utilisée dans les affichages sans innovation majeure de matériau pour obtenir des valeurs de k 1/k3 considérablement moins élevées

Stability of nematic liquid crystal configurations

This paper illustrates the use of the geodesic surface for studying the stability and bistability of nematic liquid crystal states. A liquid crystal state (or configuration) θ(z), Φ(z) defines a path on the geodesic surface. The surface is chosen such that the energy of an equilibrium configuration is proportional to the square of its path length, and hence the path of a stable state is a shortest path on the surface. The surface is helpful not only in picturing the equilibrium configurations that result from prescribed boundary conditions, but also in discussing their stability and the possibility of bistable states. This paper shows how the shape of the geodesic surface depends on the elastic constants, and uses the surface to discuss the stability of certain nematic liquid crystal states. For example, an interesting problem is the stability of the planar vertical (V) and 180° twisted (T) states proposed for displays [Boyd, Cheng, and Ngo, Appl. Phys. Lett. 36 (1980) 556]. The path of the V state is in a vertical plane through the pole of the surface, but there is a shorter path belonging to the T state if the values of θ at the boundaries are larger than a critical angle [Porte and Jadot, J. Physique 39 (1978) 213]. The geodesic surface makes apparent the existence of this critical boundary tilt bias angle, provides an easy derivation of the stability limits for the 180° twisted states with θ = π/2 and with sin2 θ = 1/2(1 — k2/k 3), and allows visualization of the energy relationships of topologically equivalent states.Cet article illustre l'utilisation de la surface géodésique pour étudier la stabilité et la bistabilité des états des cristaux liquides nématiques. Un état (ou configuration) d'un cristal liquide θ(z), Φ(z) définit un chemin sur la surface géodésique. La surface est choisie de telle sorte que l'énergie d'une configuration d'équilibre soit proportionnelle au carré de la longueur du chemin et de ce fait le chemin d'un état stable est le chemin le plus court sur la surface. La surface est utile non seulement pour illustrer les configurations d'équilibre qui découlent des conditions définies a la surface du cristal liquide, mais aussi pour discuter leur stabilité et les possibilités d'états bistables. Cet article montre comment la forme de la surface géodésique dépend des constantes élastiques et utilise la surface pour discuter la stabilité de certains états de cristaux liquides nématiques. Par exemple, un problème intéressant est la stabilité de l'état planaire vertical (V) et de l'état en hélice avec une torsion de 180° (T) proposés pour des affichages [Boyd, Cheng et Ngo, Appl. Phys. Lett. 36 (1980) 556]. Le chemin de l'état V est contenu dans un plan vertical à travers le pôle de la surface, mais il existe un chemin plus court appartenant à l'état T si les valeurs de 0 à la surface sont plus grandes qu'un angle d'inclinaison critique [Porte et Jadot, J. Physique 39 (1978) 213]. La surface géodésique rend apparente l'existence de cet angle d'inclinaison critique, apporte une dérivation aisée des limites de stabilités pour les états en hélice à 180° avec θ = π/2 et avec sin2 θ = 1/2 (1 - k2/ k3) et permet la visualisation des relations énergétiques d'états topologiquement équivalentes

Liquid crystals and geodesics

Since a unit vector n is a point on the unit sphere, any one-dimensional liquid crystal configuratior n(z), a ≤ z ≤ b, generates a path on the unit sphere. In order to see what configurations are stable, we map the unit sphere onto a surface G having the property that equilibrium configurations of a nematic liquid crystal map into geodesic lines on the surface (geodesics). The shape of the surface depends on the elastic constant ratios k1/k3 and k2/k3, and is a sphere when all three constants are equal. A picture or model of the surface for a particular material is helpful in visualizing the equilibrium configurations that correspond to prescribed boundary conditions n(a) and n(b), and in studying their energy and stability. For example, a configuration n(z) is in stable equilibrium if and only if the path on G is a curve of least length among nearby curves having the same end points, and arc length ds on G is proportional to dz. The physical interpretation of the proportionality of ds to dz is that the elastic free energy density of the liquid crystal is a constant, independent of z.Puisqu'un vecteur unitaire n est un point sur la sphère unitaire, toute configuration unidimensionnelle de cristal liquide n(z), avec a ≤ z ≤ b, engendre un chemin sur cette sphère. Pour observer quelles configurations sont stables, nous transformons la sphère unitaire en une surface G telle que les configurations d'équilibre d'un cristal liquide nématique soient transformées en des lignes géodésiques à la surface. La forme de la surface dépend des rapports de constantes élastiques k 1/k3 et k2/k3 ; c'est une sphère lorsque les trois constantes sont égales. Un modèle de la surface pour un matériau particulier est utile pour visualiser les configurations d'équilibre correspondant aux conditions de surface, prescrites n(a) et n(b), et pour étudier leur énergie et leur stabilité. Par exemple, une configuration n(z) est en équilibre stable si, et seulement si le chemin sur G est le plus court parmi ceux ayant les mêmes extrémités et si la longueur de l'arc ds sur G est proportionnelle à dz. L'interprétation physique de la proportionnalité entre ds et dz est que la densité d'énergie élastique libre du cristal liquide est une constante indépendante de z