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

From Sediment to rock: Diagenetic processes of hardground formation in deep-water carbonate mounds of the NE Atlantic

Modern cool-water carbonate mounds topped by corals form an extended reef belt along the NW European continental margin at 200–1200 m water depth. An essential element of mound growth are hardgrounds which provide a stable substratum for mound-building invertebrate colonisation and stabilise the inclined mound flanks. Evaluating the degree of lithification and the slope stability against erosion represents an important task within the ESF programme MOUNDFORCE under the umbrella of EUROMARGINS. Sampling of hardgrounds during RV Meteor cruises M61-1 and -3 in 2004 by means of the IFM-GEOMAR TV-grab and the Bremen ROV QUEST focused on carbonate mounds of the Porcupine Seabight and northwestern Rockall Bank off Ireland. Lithified carbonates of mid-Pleistocene age were exhumed during the Holocene and are now exposed on the top and flanks of numerous carbonate mounds showing a patchy to dense colonisation by living corals and associated invertebrates. The sediments, composed of foraminiferal–nannoplankton oozes and admixed mound-derived invertebrate skeletons, range from partly lithified chalks to dense micritic limestones. These wackestones to packstones clearly differ from bacterially induced authigenic carbonate crusts typical of hydrocarbon seep settings by showing current-induced sedimentary structures, a non-luminescing matrix indicating oxic pore fluids, and a marine isotopic signature lacking any depleted carbon regime which is typical of anaerobic methane oxidation. The carbonate lithification is driven by carbonate ion diffusion from supersaturated seawater into the pore fluids in the studied areas. Vigorous bottom currents were the ultimate control not only of carbonate cementation by enhancing the diffusion process and supporting a pumping mechanism, but also of hardground formation and mound shaping by exhuming lithified carbonates and preventing fine-grained sediment accumulation at the downslope mound flanks