Greens function methods

Benesh G A and Liyanage L S G 1994 Surface-embedded Green-function method for general surfaces application to Aip 11) Phys. Rev. B 49 17 264... 

Wachutka G, Fleszar A, Maca F and Scheffler M 1992 Self-consistent Green-function method for the calculation of electronic properties of localized defects at surfaces and in the bulk J. Phys. Condens Matter A 2831 Bormet J, Neugebauer J and Scheffler M 1994 Chemical trends and bonding mechanisms for isolated adsorbates on Al(111) Phys. Rev. B 49 17 242... 

Korrmga-Kohn-Rostoker Green-function method 129... 

Abstract The hadronic equation of state for a neutron star is discussed with a particular emphasis on the symmetry energy. The results of several microscopic approaches are compared and also a new calculation in terms of the self-consistent Green function method is presented. In addition possible constraints on the symmetry energy coming from empirical information on the neutron skin of finite nuclei are considered. 

Green function method, that can be considered as a generalization of the BHF approach. The results are compared with those from various many-body approaches, such as variational and relativistic mean field approaches. In view of the large spread in the theoretical predictions we also examine possible constraints on the nuclear SE that may be obtained from information from finite nuclei (such the neutron skin). 

Appendix C Mean-Field Green Function Method.155... 

The diffusion coefficients at infinite dilution (D]0, D 0, and Dr0) for the fuzzy cylinder reduce to those for the wormlike cylinder, which can be calculated as explained in Appendix B. On the other hand, these diffusion coefficients, D, Dx, and Dr, for the fuzzy cylinder at finite concentrations can be formulated by use of the mean-field Green function method and the hole theory, as detailed below. 

To explain the Green function method for the formulation of Dx, D and D, of the fuzzy cylinder [19], we first consider the transverse diffusion process of a test fuzzy cylinder in the solution. As in the case of rodlike polymers [107], we imagine two hypothetical planes which are perpendicular to the axis of the cylinder and touch the bases of the cylinder (see Fig. 15a). The two planes move and rotate as the cylinder moves longitudinally and rotationally. Thus, we can consider the motion of the cylinder to be restricted to transverse diffusion inside the laminar region between the two planes. When some other fuzzy cylinders enter this laminar region, they may hinder the transverse diffusion of the test cylinder. When the test fuzzy cylinder and the portions of such other cylinders are projected onto one of the hypothetical planes, the transverse diffusion process of the test cylinder appears as a two-dimensional translational diffusion of a circle (the projection of the test cylinder) hindered by ribbon-like obstacles (cf. Fig. 15a). 

This two-dimensional diffusion can be treated by the Green function method, which is expounded in detail in Appendix C, and shows that Dx can be... 

For an infinitely thin rodlike polymer for which d/L = de/Le = 0, we have fi = F 0 = Fx0 = D 0/D = 1, and Eq. (46) reduces to Teraoka and Hay-aka wa s original expression [107] of Dx for rodlike polymers. At high concentrations, the results from the Green function method approach the one from the cage model [107], Teraoka [110] calculated stochastic geometry and probability of the entanglement for infinitely thin rods by use of the cage model, and evaluated px to be... 

When the diffusion time is short enough, the translation on the spherical surface is approximately identical with that on the tangent plane to the spherical surface. The latter is the two-dimensional diffusion process treated by the Green function method in Appendix C, and we can use Eq. (C17) again. Since the rotational diffusion coefficient Dr is related to the translational diffusion coefficient D<2) in Eq. (Cl7) by Dr = D(2)/(Le/2)2, we have... 

The longitudinal diffusion coefficient D has been formulated by the hole theory in Sect. 6.3.2. If the similarity ratio X in this theory is chosen to be 0.025 for the rod with the axial ratio 50, Eq. (58) with Eq. (56) gives the solid curve in Fig. 16a. Though it fits closely the simulation data, the chosen X is not definitive because the change in D(l is small and the definition of the effective axial ratio is ambiguous. Though not shown here, Eq. (53) for D, by the Green function method describes the simulation data equally well if P and C, are chosen to be 1000 and 1, respectively. 

Equations (46)-(48) lead to an expression of Dx/Dx0, in which Le = L and dc = d for rodlike polymers. Since Le/de = L/d = 50, f can be equated to unity in a good approximation. Estimating Djo/Dj from Eq. (58) with X = 0.025 and Fjo/Fxo from Eqs. (B4) and (B5) in Appendix B with Le/de = L/d = 50, we have calculated Dx/Dx0 as a function of the reduced concentration L3c The results are compared with Bitsanis et al. s simulation data in Fig. 16a. It can be seen that the theoretical solid curve for D /D 0 deviates downward slightly from the simulation data points, implying that the Green function method for Dx overestimates the entanglement effect compared to Bitsanis et al. s simulation. 

The rotational diffusion coefficient can be calculated from Eqs. (50) (52) formulated by the Green function method. The Dr/Dr0 values obtained by Doi et al. for infinitely thin rods should be compared with the theory in which Le = L and D]]0/D, = F,0/F10 = fr = b The theoretical solid curve in Fig. 16b shows a favorable comparison with the simulation data. 

Recently, Doi 44) has shown that both conformational and dimensional problems of interrupted helices can be solved more simply by the use of a mathematical technique called the Green function method. His treatments may be viewed as an extension of the theory of de Gennes (45), who demonstrated the power of this method in a study of the branched structure of dAT copolymers. 

Nan and Weng (1999) have developed a Green function method to determine self-consistently the effective magnetostrictive properties of composites. The authors claim that their method, in principle, can be used to study the effects of material constants and microstructure, such as anisotropy, particle shape and orientation relative to the applied magnetic field. 

A very effective method to describe scattering and transport is the Green function (GF) method. In the case of non-interacting systems and coherent transport single-particle GFs are used. In this section we consider the matrix Green function method for coherent transport through discrete-level systems. 

This expression is equivalent to the one derived earlier by the single-particle Green function method. 

For the special case of non relativistic Hydrogen, the multiphoton transition rate can be obtained exactly using methods based on Green function techniques, which avoid summations over intermediate states. This approach was introduced in order to treat time independent problems, and later extended to time dependent ones [2]. In the Green function method, the evaluation of the infinite sums over intermediate states is reduced to the solution of a linear differential equation. For systems other than Hydrogen, this method can also be used, but the associated differential equation has to be integrated numerically. The two-photon transition rate can also be evaluated exactly by performing explicitly the summation over the intermediate states. 

Two theoretical techniques worthy of serious review here, perturbation and Green function methods, can be considered complementary. Perturbation methods can be employed in systems which deviate only slightly from regular shape (mostly from planar geometry, but also from other geometries). However, they can be used to treat both linear and nonlinear PB problems. Green function methods on the other hand are applicable to systems of arbitrary irregularity but are limited to low surface potential surfaces for which the use of the linear PB equation is permitted. Both methods are discussed here with reference to surfactant solutions which are a potentially rich source of nonideal surfaces whether these be solid-liquid interfaces with adsorbed surfactants or whether surfactant self-assembly itself creates the interface. 

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