Green-function formalism

Cerda J, van Hove MA (1997) Efficient method for the simulation of STM images. I. Generalized green-function formalism. Phys Rev B 56 15885... 

In this section, we describe our model, and give a brief, self-contained account on the equations of the non-equilibrium Green function formalism. This is closely related to the electron and particle-hole propagators, which have been at the heart of Jens electronic structure research [7,8]. For more detailed and more general analysis, see some of the many excellent references [9-15]. We restrict ourselves to the study of stationary transport, and work in energy representation. We assume the existence of a well-defined self-energy. The aim is to solve the Dyson and the Keldysh equations for the electronic Green functions ... 

Structure of the molecular device [84-87, 129] with the well-established Green function formalism, to compute the transport characteristics. In such a way, it would be possible to distinguish self-consistently in the calculations different mechanisms, and their relative importance in experimental settings. 

Two different procedures were used for the removal of the reference state singularities and the derivation of RSC. As it was shown in [12], the Coulomb-Coulomb contribution to RSC is absent. The RSC were first introduced in QED in [13] in the frames of the Green function formalism in the Feynman gauge [13,14]. The expressions for RSC are much simplified in the equal energies case (Ea = Eb), i.e. for the ground state of the two-electron ion. The explicit expression for the equal energies correction was derived in [15]... 

There is clear now that the Green function formalism do not automatically solve the initial Schrodinger problem, but replaces it with a more general one when also the causality of events counts. The passage from the retarded to advanced Green function equation can be easily made though the previously stipulated recipe. 

As example of the use of exciton theory, the visible optical spectrum of two typical polydiacetylene crystals calculated by S. Suhai (PTS with an acetylene-like structure and TCDU with a butatriene-like structure) are presented using a first principle Greenes function formalism of charge transfer exciton theory. 

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