Local Green s functions

To verify effectiveness of NDCPA we carried out the calculations of absorption spectra for a system of excitons locally and linearly coupled to Einstein phonons at zero temperature in cubic crystal with one molecule per unit cell (probably the simplest model of exciton-phonon system of organic crystals). Absorption spectrum is defined as an imaginary part of one-exciton Green s function taken at zero value of exciton momentum vector... 

TOTAL ENERGY CALCULATIONS OF ALLOYS LOCALLY SELF-CONSISTENT GREEN S FUNCTION METHOD... 

To improve the latter a number of 0 N) methods have been recently proposed but practically all of them exploit Hamiltonian formalism. However, in Refs. 4,5 the locally self-consistent multiple scattering (LSMS) method based on the real space multiple scattering theory has been outlined, and in Ref. 6 its central idea in the form of the local interaction zone (LIZ) was incorporated into the Green s function technique, leading to the locally self-consistent Green s function method (LSGF). 

Figure 2. Total energies of ordered (LIq structure, squares), random (circles) and segregated (triangles) fee RhsoPdso alloys as a function of the number of neighboring shells included in the local interaction zone. Values obtained by the LSGF-CPA method are shown by filled symbols and full lines. The energies obtained by the reference calculations are shown by a dashed line (LMTO, ordered sample), a dotted line (LMTO-CPA, random sample), and a dot-dashed line (interface Green s function technique, segregated sample).

I.A. Abrikosov, A.M.N. Niklasson, S.I. Simak, B. Johansson, A.V. Ruban, and H.L. Skriver, Order-N Green s function technique for local environment effects in alloys, Phys. Rev. Lett. 76 4203 (1996). 

Hoshino et al. (1989) have recently carried out spin-density-functional calculations for anomalous muonium in diamond. They used a Green s function formalism and a minimal basis set of localized orbitals and found hyperfine parameters in good agreement with experiment. 

Stepanyuk et al. [471] have applied local approximation of the density-functional theory and the Korringa-Kohn-Rostoker (KKR) Green s function method to determine the energy of Co adatoms located at the ideal Au(lOO) surface. Total-energy calculations have shown that Co atoms and small Co clusters are preferably embedded inside the substrate. 

The other type of theory uses non-equilibrium Green s functions. Green s functions are more tractable in a localized basis set, such as the one... 

For arbitrary initial conditions, the solution of (4.27) may be derived from the knowledge of the response, at an arbitrary site m, to an excitation localized at t = 0 on an arbitrary site n (this is the Green s function of the system see Appendix A). As we are interested in spectral data, it is natural to use the Fourier transform of (4.27) corresponding to an initial condition of one excitation localized on site n> ... 

The parameter p should be a function of local interaction which is related to the non-zero v mentioned in Eqs. (7) and (8). Let us consider the hole density-density correlation function and write the Green s function... 

The theoretical study of the lattice dynamics of the defective crystals conventionally makes use of the local vibrational density of states (LVDS) gia(ro) It is related to the diagonal element of the Green s function Guia(co) by the expression ... 

In Fig. 5 LVDS projected onto displacements with Ai-symmetry of the center ion and the 0 z) ion for ZnO Ni crystals are presented. Specific features of the symmetrized LVDS in a defective crystal, which differ from those of the symmetrized LVDS in a perfect crystal, corresponded to both resonant vibrations and gap vibrations induced by defects. Local vibration frequencies were determined by observing the change of the sign of the real part of the Green s function. For example, the resonant vibration located in the acoustic band at the fiequency 3.0 THz (see Fig.5a) is associated with motion of the Ni impurity. 

This is the definition of the Green s function of a local, central potential. The solution of (7.135) is... 

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