The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Normative equations for central augmentation index:Assessment of inter-population applicability and how it could be improved

Common reference values of arterial stiffness indices could be effective screening tool in detecting vascular phenotypes at risk. However, populations of the same ethnicity may differ in vascular phenotype due to different environmental pressure. We examined applicability of normative equations for central augmentation index (cAIx) derived from Danish population with low cardiovascular risk on the corresponding Croatian population from the Mediterranean area. Disagreement between measured and predicted cAIx was assessed by Bland-Altman analysis. Both, cAIx-age distribution and normative equation fitted on Croatian data were highly comparable to Danish low-risk sample. Contrarily, Bland-Altman analysis of cAIx disagreement revealed a curvilinear deviation from the line of full agreement indicating that the equations were not equally applicable across age ranges. Stratification of individual data into age decades eliminated curvilinearity in all but the 30–39 (men) and 40–49 (women) decades. In other decades, linear disagreement independent of age persisted indicating that cAIx determinants other than age were not envisaged/compensated for by proposed equations. Therefore, established normative equations are equally applicable to both Nordic and Mediterranean populations but are of limited use. If designed for narrower age ranges, the equations’ sensitivity in detecting vascular phenotypes at risk and applicability to different populations could be improved

Does dairy food intake predict arterial stiffness and blood pressure in men? Evidence from the Caerphilly prospective study

Arterial stiffness is an independent predictor of cardiovascular disease events and mortality, and like blood pressure, may be influenced by dairy food intake. Few studies have investigated the effects of consumption of these foods on prospective measures of arterial stiffness. The present analysis aimed to investigate the prospective relationship between milk, cheese, cream, and butter consumption and aortic pulse wave velocity, augmentation index, systolic and diastolic blood pressure, as well as cross-sectional relationships between these foods and systolic and diastolic blood pressure and metabolic markers using data from the Caerphilly Prospective Study. Included in this cohort were 2512 men, aged 45 to 59 years, who were followed up at 5-year intervals for a mean of 22.8 years (number follow-up 787). Augmentation index was 1.8% lower in subjects in the highest quartiles of dairy product intake compared with the lowest (P trend=0.021), whereas in the highest group of milk consumption systolic blood pressure was 10.4 mm Hg lower (P trend=0.033) than in nonmilk consumers after a 22.8-year follow-up. Cross-sectional analyses indicated that across increasing quartiles of butter intake, insulin (P trend=0.011), triacylglycerol (P trend=0.023), total cholesterol (P trend=0.002), and diastolic blood pressure (P trend=0.027) were higher. Across increasing groups of milk intake and quartiles of dairy product intake, glucose (P trend=0.032) and triglyceride concentrations (P trend=0.031) were lower, respectively. The present results confirm that consumption of milk predicts prospective blood pressure, whereas dairy product consumption, excluding butter, is not detrimental to arterial stiffness and metabolic markers. Further research is needed to better understand the mechanisms that underpin these relationships