Hubbard Model with Inter-Site Kinetic Correlations

We introduced the inter-site electron-electron correlation to the Hubbard III approximation. This correlation was excluded in the Hubbard III approximation and also in the equivalent coherent potential approximation. Including it brings two spin dependent effects: the bandwidth correction and the bandshift correction, which both stimulate the ferromagnetic ground state. The bandshift correction factor causes an exchange splitting between the spin-up and spin-down spectrum, and its role is similar to the exchange interaction in the classic Stoner model. The spin dependent bandwidth correction lowers the kinetic energy of electrons by decreasing the majority spin bandwidth for some electron occupations with respect to the minority spin bandwidth. In certain conditions it can lead to ferromagnetic alignment. A gain in the kinetic energy achieved in this way is the opposite extreme to the effect of a gain in potential energy due to exchange splitting. The bandshift factor is a dominant force behind the ferromagnetism. The influence of the bandwidth factor is too weak to create ferromagnetism and the only result is the correction to the classic coherent potential approximation in favor of ferromagnetism.Comment: 29 pages, 5 figure

Alternative equation of motion approach to the single-impurity Anderson model

Solving the single-impurity Anderson model (SIAM) is a basic problem of solid state physics. The SIAM model is very important, at present it is also used for systems with quantum impurities, e.g. semiconductor quantum dots and molecular transistors. Its main application is in the scheme of dynamical mean field theory (DMFT) describing strong correlation electron systems. To solve the SIAM problem we use the equation of motion (EOM) Green function approach. In this report we present the novel EOM approximation in which we differentiate the Green function over both time variables. This differs from the commonly used EOM solution by Appelbaum, Penn and Lacroix where the authors take time derivative only over primary time variable. After extending calculations to higher order Green functions we find the new approximate dynamical solution of SIAM. The results are compared with the solutions to the SIAM problem at intermediate Coulomb repulsion U such as the Modified Iterative Perturbation Theory. Our approach is suitable for describing quantum dots.Comment: 6 pages, 3 figure

Magnetic ordering of itinerant systems in modified mean field theory: antiferromagnetism

We analyze the itinerant model for antiferromagnetism, which was developed previously by Plischke, Mattis, Brouers and Mizia. In this model we include both; single-site and two-site electron correlations. Including additionally band degeneration into the model allows for considering intra-atomic exchange interactions in the Hamiltonian. The modified Hartree-Fock approximation for the two-site interactions is used. This approximation gives the spin band narrowing, which is the same for both spin directions and affects possibility of antiferromagnetic ordering. We use the Green function technique and CPA decoupling. This allows for the change in shape of the spin bands, described by the correlation factors, which decreases kinetic energy of the system. The effective Hartree field and the gain in kinetic energy due to the on-site and inter-site correlation factors drive the antiferromagnetism.Comment: 8 pages, 1 figur

Antiferromagnetic ordering of itinerant systems in modified mean-field theory

This is an analysis of the itinerant model for antiferromagnetism, in which is included both on-site and inter-site electron correlations. We also consider the band degeneration, which brings into the Hamiltonian the on-site exchange interactions. The Green function technique is used and the coherent potential approximation (CPA) decoupling for the on-site Coulomb repulsion. This decoupling combined with the modified Hartree-Fock approximation for the inter-site interactions generates the change in shape of the spin bands with growing interaction constants, which is described by the correlation factors and which decreases the kinetic energy of the system. The effective Hartree field and the gain in kinetic energy due to the on-site and inter-site correlation factors drive the antiferromagnetism. The on-site and inter-site interactions act together towards the antiferromagnetism. Their cooperation decreases the interaction constants required for the antiferromagnetic ordering. This new approach allows for the antiferromagnetic instability in the purely itinerant model at the half-filling in the split band limit. This situation describes the high temperature superconducting cuprates.Comment: 26 pages, 9 figure

Assessing the innervation of the dorsal wrist capsule using modified Sihler's staining

Background: The aim of this study was to assess the innervation of the dorsal articular capsule of the wrist using modified Sihler’s staining. Materials and methods: Thirty dorsal wrist capsules were collected from 15 donors (both sides) within 12 hours of death. All the capsules were collected in the same manner - using the dorsal incision. The specimens were stained according to the protocol of the modified Sihler’s staining technique. The preserved capsules were analysed under 8-16× magnification of an optical microscope for the presence of major nerve trunks, their major and minor branches, and nerve connections. Results: The range of innervation visualised was that the posterior interosseous nerve innervated approximately 60% of the central part; the remaining area was innervated by the dorsal sensory branch of the radial nerve and medial antebrachial cutaneous nerve. The constant findings were the branches departing from the ulnar side of the posterior interosseous nerve and from the radial side, with an exception seen in 2 cases. A communicans branch between the posterior interosseous nerve and medial antebrachial cutaneous nerve was seen in all the specimens. The posterior interosseous nerve innervation extended beyond the level of the carpometacarpal joints II-V. Conclusions: The modified Sihler’s staining technique allows for transparent visibility of the nerves that innervate the dorsal wrist capsule. However, it does not allow as accurate assessment as does histological examination, especially regarding the evaluation of nerve endings. Nevertheless, this method provides a significantly larger area of nerve observation than is provided by histological examination