Second derivative of the log-likelihood in the model given by a Levy driven stochastic differential equations

By means of the Malliavin calculus, integral representation for the second derivative of the loglikelihood function are given for a model based on discrete time observations of the solution to SDE driven by a Levy process.Comment: arXiv admin note: substantial text overlap with arXiv:1301.514

Malliavin calculus approach to statistical inference for Levy driven SDE's

By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation dX_t=a_\theta(X_t)dt + dZ_t with a tempered \alpha-stable process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved

Model for the electronic structure, Fermi arcs, and pseudogap in cuprate superconductors

We suggest a model for electronic structure of cuprate superconductors that makes it possible to describe evolution of this structure with the doping and provides a new explanation for a number of typical features of cuprates, including the pseudogap and the Fermi arcs. According to this model, the unique electronic structure of cuprates is favorable for the formation of two-atomic negative-U centers (NUCs) and realization of a peculiar mechanism of the electron-electron interaction.Comment: 9 pages, 4 figure

On the possible common nature of the ground state in Cu- and Fe-based HTSCs

A qualitative model describing the ground state and the mechanism of superconducting pairing in Cu- and Fe-based high-temperature superconductors (HTSCs) is suggested. In this model, doping by localized charges (as well as physical or chemical pressure) is supposed to be responsible for transition of Cu- and Fe-based HTSC to new ground state common for both HTSC classes where specific mechanism of superconductivity takes place. The resulting HTSC ground state is strongly correlated insulator with not fully filled exciton-electronic band, where the incoherent electron transport is impossible but coherent superconducting transport is possible because the band is not fully occupied. It is shown also that such electronic system is inherently predisposed to superconductive pairing because each pair of nearest cations acts as a two-atom negative-U center. The nature of Fermi arcs and mechanism of pseudogap are considered. It is shown that both of these features result from d-wave pairing and therefore have to be observed only in cuprates. We believe that the considered ground state is common for various families of HTSCs including cuprates, pnictides, selenides, bismutates and probably some other.Comment: 16 pages, 7 figures; abstract, text and figures modified, typos corrected. arXiv admin note: substantial text overlap with arXiv:1011.3623 and arXiv:1007.032

Insulator-metal transition in high-Tc_c superconductors as result of percolation over -U centers

The mechanism of -U center formation in high-$T_{c}$ superconductors (HTS) with doping is considered. It is shown that the transition of HTS from insulator to metal passes through the particular dopant concentration range where the local transfer of singlet electron pairs from oxygen ions to pairs of neighboring cations (-U centers) are allowed while the single-electron transitions are still forbidden. We believe it is this concentration range that corresponds to the region of high-Tc superconductivity and the interelectron attraction results from the interaction of electron pairs with -U centers. Additional hole carriers are generated as the result of singlet electron pair transitions from oxygen ions to -U-centers. The orbitals of the arising singlet hole pairs are localized in the nearest vicinity of -U center. In such a system the hole conductivity starts up at the dopant concentration exceeding the classical 2D-percolation threshold for singlet hole pair orbitals. In the framework of the proposed model the phase diagram Ln-214 HTS compounds is constructed. The remarkable accord between calculated and experimental phase diagrams may be considered as the confirmation of the supposed model. The main features of hole carriers in HTS normal state are found to be the nondegenerate distribution and the dominant contribution of electron-electron scattering to the hole carrier relaxation processes. Various experimentally observed anomalies of HTS properties are shown to be the consequences of the above-mentioned features. The conclusion is made that HTS compounds are the special class of solids where the unusual mechanism of superconductivity different from BCS is realized.Comment: 8 pages, 6 figure

Phase diagrams of La2-xSrxCuO4 and YBa2Cu3O{6+/delta} as the keys to understanding the nature of high-Tc superconductors

The model that explains many of the details of superconducting and magnetic phase diagrams of YBa2Cu3O{6+/delta} and La2-xSrxCuO4 is presented. The model is based on the assumption of rigid localization of doped charges in the close vicinity of doped ion. This localization results in local variation of electronic structure of the parent charge-transfer insulator that depends on the local mutual arrangement of the doped charges. It is shown that in such system the negative-U centers (NUCs) may form under certain conditions on the pairs of neighboring Cu cations in CuO2 plane. We consider the mechanism of hole generation. The calculated dependences of hole concentration in YBa2Cu3O{6+/delta} on doping and temperature are found to be in a perfect quantitative agreement with experimental data. In the framework of the model the phase diagrams of YBa2Cu3O{6+/delta} is considered and the interpretation of pseudogap and 60 K-phases in YBa2Cu3O{6+/delta} is offered. The pseudogap has superconducting nature and arises at temperature T*>Tc/inf>Tc in small clusters uniting a number of NUCs due to large fluctuations of NUC occupation. (Tc/inf and Tc are the temperatures of superconducting transition for infinite and finite clusters, accordingly). The calculated T*(/delta) and Tc(/delta) dependences are in accordance with experiment. The range between T*(/delta) and Tc(/delta) corresponds to the range of fluctuations where small clusters fluctuate between superconducting and normal states owing to fluctuations of NUC occupation. The phase diagram of La2-xSrxCuO4 is calculated. It is shown the features of the superconducting phase diagram and the characteristics of stripe textures of La2-xSrxCuO4 only reflect the geometrical relations existing in a square lattice and the competition of different types of dopant ordering.Comment: 26 pages, 17 figures. New references are include

Towards the issue of the origin of Fermi surface, pseudogaps and Fermi arcs in cuprate HTSCs

Earlier we have proposed a new approach to the analysis of superconducting phase diagrams for cuprates and pnictides and have shown that the positions of superconducting domes on the diagrams can be predicted with high accuracy proceeding from only the crystal structure of a particular compound. The proposed approach uses the concept of the self-localization of doped carriers due to their formation of trion complexes that represent a bound state of the doped carrier and charge transfer excitons emerging under its influence. Here, as exemplified by cuprates, we show that the use of the proposed approach to the analysis of the transformation of an electronic structure with doping enables an explanation to a range of their anomalies: Fermi arcs, large and small pseudogaps etc. The basic conclusion is that the role of the Fermi surface in cuprates is played by an isoenergetic contour that emerges at the sectioning of the surface of a band dispersion by a dispersionless "biexciton" pair level. This level additionally plays the role of an acceptor to lead to the emergence of hole carriers on the isoenergetic contour and to a jump of the chemical potential. Based on the conducted consideration, we propose a possible mechanism of superconducting pairing genetically inherent in such a system.Comment: 13 pages, 5 figures, typos correctio

Superconducting phase diagrams of cuprates and pnictides as a key to the HTSC mechanism

This paper reviews experimental phase diagrams of cuprates and pnictides to demonstrate that specific features of the superconducting phase diagrams in bothHTSC families can be understood within the framework of the proposed approach,which assumes the formation, under heterovalent doping, of localized trion complexes consisting of a doped carrier and charge transfer (CT) excitons. The geometry of such cells containing CT excitons (CT plaquettes) in the basal plane of the crystal is determined by its crystal structure and the type of dopant, so that the dopant concentration range corresponding to the existence of a percolation cluster of CT plaquettes can be readily determined for each particular compound. These dopant concentration ranges coincide with good accuracy with the experimental ranges of superconducting domes in the phase diagrams of the HTSC compounds considered. The generation of free carriers and the mechanism of superconducting pairing in this pattern is related to biexciton complexes (Heitler-London centers) emerging in neighboring CT plaquettes.Comment: 15 pages, 13 figure

Parameter estimation in models generated by SDE's with symmetric alpha stable noise

The article considers vector parameter estimators in statistical models generated by Levy processes. An improved one step estimator is presented that can be used for improving any other estimator. Combined numerical methods for optimization problems are proposed. A software has been developed and a correspondent testing and comparison have been presented

On the possible mechanism of superconductivity in cuprates and pnictides

The nature of the normal state and the mechanism of superconductivity in two families of high-temperature superconductors, cuprates and pnictides, remain a matter of intense discussions. According to band-structure calculations, confirmed by ARPES data, the electronic structure of pnictides differs considerably from that of cuprates. However, in spite of these differences, it looks like in both cases there exists some general and fairly "coarse" mechanism independent of fine details of the band structure and responsible for superconductive pairing in these materials. Here, we suggest a qualitative model describing the ground state and the mechanism of superconductive pairing in cuprates and pnictides that, in our opinion, can explain many of their unusual properties.Comment: 6 pages, 1 figure, submitted to FPS`11, 3-7 October 2011, Zvenigoro