Single particle Green function

Coherent transport single-particle Green functions... 

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

In terms of Green s functions, what we have just described can be expressed by saying that, for example, by studying the equation of motion of the single-particle Green function,... 

Here, is the retarded single-particle Green function,... 

Figure 2 Exact single-particle spectrum (solid line) for four electrons on a four-site ring compared with the results of a GW approximation (dash-dotted line) and those obtained from an effective two-particle Green-function (dashed line) for U — 1.0.

The zeroth-order wavefunction of an excited state in an extended system cannot be described by a single determinant since the energies of the excited determinants form continuous bands. The states associated with the same band are degenerate since the energy difference between two adjacent states is an infinitesimal number. Thus, to calculate the energy spectrum of excited states, one needs to use degenerate MBPT, two-particle green function theory or a method like EOM-CC [5],... 

One way to obtain the single-particle Green s function is via solution of what is called Dyson s equation [21, 48, 49],... 

Note that expressions like two-particle operator and single-particle Green s function refer to the number of particles involved in the definition of the operator (two in the case of an interaction, one for a potential energy, etc.), not to the total number of particles present in the system. 

The single-particle Green s function is related to the irreducible self energy by Dyson s equation (38) and to the two-particle Green s function by the equation of motion (37). It can also be related to the xc potential of DFT by the Sham-Schliiter equation [50]... 

The structure of reduced density matrices is quite simple all coordinates that 7 does not depend upon are set equal in T and T, and integrated over. The single-particle density matrix can also be considered the time-independent form of the single-particle Green s function, since it can alternatively be obtained from... 

Many of the algebraic properties of the single-particle Green s function, in particular Dyson s equation, are transferable to two-particle propagators if they are constructed starting from an orthonormal set of primary states. In this paper we will construct propagators Q(u)) with the help of the extended... 

The self energy (ni) hcts a similar analytic structure to the common self energy [25,26] of the single-particle Green s function [11] in having single poles... 

The case of the extended particle-particle Green s function in comparison with the single-particle Green s function has already been discussed in Ref. [10]... 

Thus, the single-particle Green s function can be written as the resolvent of an energy-dependent effective Hamiltonian ... 

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