Lehmann representation

Here we prove this relation using Lehmann representation - quite useful method in the theory of Green functions. The idea of the method is to use exact many-particle eigenstates n), even if they are not explicitly known. 

In the strong-coupling region, the SDW response dominates, as expected from the result of 5 = 1 for the first-excited state (see Fig. 9). The decrease of the SCPO and SCPl responses can be understand in terms of the Lehmann representation of /P as... 

We consider the simplest case for which Xip = Xo- The Lehmann representation of Xois... 

If such a truncated basis set i> is used in the actual calculations, the resulting spectral function p (e) has a Lehmann representation similar to (50) but with exact (JV — l)-electron eigenstates and eigenvalues replaced by the approximate eigenstates n,(iV - 1)> and eigenvalues E N — 1) obtained by diagonalizing H in the truneated spaee This representation shows that independently of the quality... 

The density response function can be written in the Lehmann representation... 

As commented, the Green s function contains the information about one-particle excitations (we will see in Sect. 5.4 how to obtain ground-state properties). We start from the Lehmann representation of the Green s function ... 

Figure 1. Structure Dickerson dodecamer [9] (left) and prealbumin dimer [10] (right bottom) (Langridge s first examples [11] of electrostatic potential visualizations in combination with skeletal and transparent CPK presentation) as molecular biological structural representatives of the nucleoprotein system, but also as biological representations of individual and relatedness within the frame of structure-phase transitions familiarities between early universe structure computer simulations [12] and cholesteric texture paintings by Lehmann [13,14] (right top).

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