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

Biodiversity and structure of spider communities along a metal pollution gradient

The objective of the study was to determine whether long-term metal pollution affects communities of epigeal spiders (Aranea), studied at three taxonomic levels: species, genera, and families. Biodiversity was defined by three indices: the Hierarchical Richness Index (HRI), Margalef index (DM) and Pielou evenness index (J). In different ways the indices describe taxa richness and the distribution of individuals among taxa. The dominance pattern of the communities was described with four measures: number of dominant species at a site, percentage of dominant species at a site, average dominant species abundance at a site, and the share of the most numerous species (Alopecosa cuneata) at a site. Spiders were collected along a metal pollution gradient in southern Poland, extending ca. 33 km from zinc and lead smelter to an uncontaminated area. The zinc concentration in soil was used as the pollution index.The study revealed a significant effect of metal pollution on spider biodiversity as described by HRI for species (p = 0.039), genera (p = 0.0041) and families (p = 0.0147), and by DM for genera (p = 0.0259) and families (p = 0.0028). HRI correlated negatively with pollution level, while DM correlated positively. This means that although broadly described HRI diversity decreased with increasing pollution level, species richness increased with increasing contamination. Mesophilic meadows were generally richer. Pielou (J) did not show any significant correlations. There were a few evidences for the intermediate disturbance hypothesis: certain indices reached their highest values at moderate pollution levels rather than at the cleanest or most polluted sites