Green’s function formalism

Bagrets A, Papanikolaou N, Mertig I (2007) Conduction eigenchannels of atomic-sized contacts ab initio KKR Green s function formalism. Phys Rev B 75(23) 235448... 

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. 

In this section we explicitly demonstrate how the antiresonant line shapes characteristic of configuration interaction between a discrete BO state and BO continuum can be obtained from the Green s function formalism. We restrict attention to the case of one discrete BO state interacting with one BO continuum. We shall assume that the ground state is connected to both the discrete BO state and the BO continuum by nonvanishing dipole matrix elements. 

Renner-Teller Interaction Matrices and Green s Function Formalism... 

We now study the disordered effective hamiltonian (4.4). Since a direct diagonalization of (4.4) is too hard, we shall have to use approximations which are conveniently expressed in the resolvent (or Green s function) formalism. The translation-invariant K sum in HeU is restricted to the optical wave vectors only (for K oj/c, RK / K 0I)- Therefore, it is possible to restrict the problem to this small part of the Brillouin zone using the projector operator... 

The problems associated with defects are quite numerous, and a wealth of theoretical techniques have been devised for their solution. We shall confine our attention to the Green s function formalism because of both the level of accuracy and sophistication of recent applications.and the promise that memory function methods hold in this field. 

The Green s-function formalism for impurities in its fully self-consistent formulation or in some simplified version has been used to treat short-range defect potentials. In this case the operator equations can be represented by a small basis set, restricted essentially to the impurity subspace. In addition to the matrix elements of U, one must calculate the matrix elements of G°( ). The latter are independent of the impurity disturbance and need only be calculated in the impurity subspace. Since the operator refers to the perfect crystal, it can be diagonalized with the standard methods of band the-... 

Summing up, we see that the traditional approach to impurity problems within the Green s-function formalism exploits the basic idea of splitting the problem into a perfect crystal described by the operator and a perturbation described by the operator U. The matrix elements of < are then calculated, usually by direct diagonalization of or by means of the recursion method. Following this traditional line of attack, one does not fully exploit the power of the memory function methods. They appear at most as an auxiliary (but not really essential) tool used to calculate the matrix elements of... 

The Green s function formalism alluded to in Sect. 5 can be employed to provide general expressions for kn r (s) in the statistical limit as >6,17,44)... 

Sanvito, S., Lambert, C.J., Jefferson, J.H. and Bratkovsky, A.M. (1999) General Green s-function formalism for transport calculations with spd Hamiltonians and giant magnetoresistance in Co- and Ni-based magnetic multilayers. Phys. Rev. B, 59, 11936-11948. 

Moreover, recent calculations made on a computer by using the Green s function formalism allowed theoreticians to reach the sixth-order5 (see Chapter 12, Section 3.2.5). 

A computational approach was not only very successful in fullerene research, but advances in these studies have created the demand for the development of new theoretical methods. The last part of this chapter describes the application of the non-equilibrium Green s function formalism to the investigation of the current-voltage dependence of the fullerene molecule. This method can be also q>plied to a wide range of nanomolecular devices. 

The limit in Eq.(2.145) may be chosen as well e — —0. The sign becomes important if the Green s function formalism is used in the study of time-dependent phenomena to be discussed later. Here we have to choose it once and then consistently maintain it. The function is defined as ... 

We present a theoretical methodology suitable for analyzing optical data of complex macromolecular systems. The system of interest is modeled with an effective Hamiltonian of a multilevel-multimode vibronic surface. The experimental observables are directly obtained from the thermally averaged Green s function of the model Hamiltonian. Section 1 describes the Green s function formalism and its utilities for computing various optical responses. In Section 2, we discuss modeling the photosynthetic bacterial reaction center and summarize the simulation results in Section 3. 

For entangled iV-state transfer processes, the hierarchy Green s functions formalism involves tensors each having elements. As far as the kinetics regime is concerned, however, many interesting rate processes proceed practically in a step-wise manner. In this case the kinetics rate matrix could be determined by the individual rates between two states. Remarkably, the hierarchy Green s functions for the modified ZE/HEOM is analytically solvable for two-state systems. The resulting analytical expression of rate resolution, K/,j[s), for individual elementary a) b rate process can therefore be used to construct the NxN kinetics rate matrix. 

Again to save space, some other related methods such as Green s function formalism or the diagrammatic perturbation theory, which are usually treated with second quantization on an equal footing, are not presented here. Merely the second quantized approach (particle number representation) will be elaborately discussed. However, a short review of some recent developments partly connected to the author s own work is included to illustrate the value and actuality of second quantization. 

The Green s function formalism for non-inertial elastic problems will now be used to express uf (r, 03, t), CO, t) at any point in the body, in terms of specified surface quantities. The development of this formalism is standard and will not be discussed here. We refer to the treatment by Lardner (1974) for example. Really, all that is required in the present context is that the displacements and stresses can be expressed as space integrals of the boundary functions. 

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