Quasiparticle approximation

Figure 2. Comparison of the pressure, in units of the free pressure, of the SU(3) plasma from the HTL quasiparticle approximation (7) vs. lattice data [6].

We simplify the equations and obtain some analytical results in the vibronic quasiparticle approximation, which assumes weak electron-vibron coupling limit and weak external dissipation of vibrons ... 

Additionally to the vibronic quasiparticle approximation, the electronic quasiparticle approximation can be used when the coupling to the leads is weak. In this case the lesser function can be parameterized through the number of electrons Fv in the eigenstates of the noninteracting molecular Hamiltonian H(0)... 

Neglecting off-diagonal elements of the self-energy matrix in the canonical Hartree-Fock basis in (1.15) constitutes the quasiparticle approximation. With this approximation, the calculation of EADEs is simplified, for each KT result may be improved with many-body corrections that reside in a diagonal element of the self-energy matrix. 

The quasiparticle approximation has succeeded in the description of valence ionization spectra of many systems. Recently, it has been shown that reliable results also can be obtained for core electron binding energies [26], In this section, we will describe some recent developments that have been realized with the quasiparticle approximation. 

RI methods also can be applied to electron propagator calculations in the quasiparticle approximation [28], Savings in storage are dramatic. When compared to semi-direct algorithms [21, 22], the pre-factor for RI results in a considerable speed-up. The implementation is also much simpler. Test calculations with different approximations and basis sets show the reliability of this approach. 

Keywords electron propagator quasiparticle approximations renormalized approximations quasiparticle virtual orbitals C60 fullerene ionization energies correlation states nucleotide electron detachment energies... 

Practical calculations require approximations in the self-energy operator. Perturbative improvements to Hartree-Fock, canonical orbital energies can be generated efficiently by neglecting off-diagonal matrix elements of the selfenergy operator in this basis. Such diagonal, or quasiparticle, approximations simplify the Dyson equation to the form... 

Formulas for quasiparticle approximations can be derived in two ways. The first approach arises [7,11] from older, many-body concepts that are related to quantum field theory [12,13]. Pictorial representations of self-energy expressions take the form of Feynman, Goldstone [14], or Huhengoltz [15] diagrams. After a first presentation of the OVGF approximation [16], a more flexible formulation followed [7], Detailed numerical procedures have also been described [17]. 

If the quasiparticle approximation works well, then this is a sign that the independent particle model is trustworthy. If one is looking for manifestations of the many-electron character of atoms, then the greatest interest attaches to situations where in fact the quasiparticle picture begins to break down. From this perspective, the excitation of very deep inner shells is not the most interesting situation it is more likely that the concept of a hole will lose validity for the outermost inner shells, although the situations in which this occurs are actually quite specific. 

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