The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in c
uprates, started in [Gh. Adam, S. Adam, J. Phys. A: Math. Theor., Vol.40, 11205 (2007)]. Discussion of the $(delta, T)$ phase diagram of the model points to the divergence of the energy spectrum in the limit of vanishing doping $delta$. Finite energy spectra at all possible doping rates $delta$ are obtained provided the hopping part of the effective Hamiltonian is renormalized with an effective factor pointing to the site-pairs availability for fermion hopping processes.
The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the Hubbard ope
rator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, an approximation procedure based on the identification and elimination of exponentially small quantities is described. It secures the reduction of the correlation order to GMFA-GF expressions.
The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer, is the firs
t from a set of hierarchically ordered criteria allowing a priori Bayesian inference on efficient mesh generation in automatic adaptive quadrature.
The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$Tsb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlati
on functions describing respectively the singlet hopping and the superconducting pairing. Rigorous derivation of their values is reported based on the finding that specific invariant classes of polynomial Green functions in terms of the Wannier overlap coefficients $ usb{ij}$ exist.
The detection of insufficiently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the profile of the integrand at the quadrature knots which
allows inferences approaching the theoretical 100% rate of success, under error estimate sharpening. The proposed procedure is of the highest interest for the solution of parametric integrals arising in complex physical models.
A subtractionless method for solving Fermi surface sheets ({tt FSS}), from measured $n$-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron-electron annihilation radiation ({tt 2D-ACAR}) technique, i
s discussed. The window least squares statistical noise smoothing filter described in Adam {sl et al.}, NIM A, {bf 337} (1993) 188, is first refined such that the window free radial parameters ({tt WRP}) are optimally adapted to the data. In an ideal single crystal, the specific jumps induced in the {tt WRP} distribution by the existing Fermi surface jumps yield straightforward information on the resolved {tt FSS}. In a real crystal, the smearing of the derived {tt WRP} optimal values, which originates from positron annihilations with electrons at crystal imperfections, is ruled out by median smoothing of the obtained distribution, over symmetry defined stars of bins. The analysis of a gigacount {tt 2D-ACAR} spectrum, measured on the archetypal high-$T_c$ compound $YBasb{2}Cusb{3}Osb{7-delta}$ at room temperature, illustrates the method. Both electronic {tt FSS}, the ridge along $Gamma X$ direction and the pillbox centered at the $S$ point of the first Brillouin zone, are resolved.
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization
errors on the frequency parameter of the oscillatory functions show that the accuracy gain of the present formulas over those based on the exponential fitting approach [L. Ixaru, Computer Physics Communications, 105 (1997) 1--19] is overwhelming.
