Seminář se koná každé úterý v 10:40 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičách 2, Praha 8
X-ray diffraction from crystals consisting of randomly stacked monoatomic or monomolecular layers have been investigated for several decades. Recently, these structures are again in focus of attention, since new materials like topological insulators, multiferroic systems etc. exhibit a random layered structure. An x-ray diffraction experiment from a random stack of monolayers can be carried out in two basic arrangements; in a standard set-up the measured diffracted intensity is collected from a large sample volume, for which the ergodic hypothesis applies, so that the measured signal is averaged over a statistical ensemble of all possible monolayer distributions (microstates). Synchrotron x-ray sources can deliver very narrow and almost coherent x-ray beams, allowing for another experimental set-up, in which only one microstate is irradiated. The application of a fully coherent beam makes it possible to retrieve the phase of the diffracted beam and determine fully the monolayer sequence under investigation. We have used both experimental approaches for the investigation of epitaxial layers of rhombohedral topological insulators (Bi2Se3, Bi2Te3), for the investigation of stacking faults in non-polar GaN layers and for the study of wurtzite and zincblende segments in III-V nanowires.
The density-functional theory is a powerful tool for modeling the electronic structure of crystalline solids and for computational prediction of materials' properties. There are, however, whole classes of compounds, for which the present-day approximate implementations of the density-functional theory do not reach sufficient accuracy. Among the problematic cases are compounds with strongly correlated electrons, for instance those that contain elements from the lanthanide or actinide groups. A substantially improved description of the electron-electron correlations is achieved by building a material-specific Hubbard model on the top of the density-functional result, and by solving this model by means of the dynamical mean-field theory. I show how such framework can be used to analyze core-level spectra on the same footing as the valence-band electronic structure. I use photoemission from core levels in actinide and rare-earth oxides as an illustration, and discuss how the satellite features observed in the photoelectron spectra do (or do not) reflect the chemical bonding.
The standard models of economics and finance make some extremely convenient but unjustified assumptions about the aggregated behaviour of the participants within the system. These greatly simplify the mathematics required to the point where many mathematicians do not even consider them interesting research areas.
I shall describe some non-standard financial market models, both agent-based and mesoscopic in nature, and their relationship to, if time permits: Coupled PDEs with very unusual boundary conditions Queueing Theory Generalized Polya urns Variants of self-organized criticality models
Jiří Horáček Jiří Bičák