Quasiparticle methods

In practice, approximations in the self-energy operator are needed. Efficient, perturbative improvements to Koopmans results may be produced by the neglect of off-diagonal matrix elements of the self-energy operator in the canonical, Hartree-Fock basis. Such diagonal approximations in the selfenergy, which are also known as quasiparticle methods, yield an especially simple form of the Dyson equation. 

One approach to the derivation of quasiparticle methods departs [9, 13] from many-body concepts that themselves arose from quantum field theory [4, 14]. Terms in the self-energy may be represented pictorially in terms of Feynman, Goldstone [15], or Hugenholtz [16] diagrams. An initial presentation of the OVGF approximation [17] was followed by a more flexible formulation [9]. Numerical procedures have been described in detail [18]. 

Nuclear Theory The Quasiparticle Method, 1968 The Quark Model, 1969... 

This model, as wets discussed in Chap.6, gives one an opportunity to describe the kinetics of non-ideal gas media in static and fluctuating surface field. Therefore, when approximating the kinetic operators (6.2.4), (6.2.5) one can use the results of quasiparticle method for non-ideal media kinetics (Dubrovskiy and Bogdanov 1979b), theory of liquids (Croxton 1974), theory of Brownian motion (Akhiezer and Peletminskiy 1977), theory of phase transitions, models of equilibrium properties of such systems (Jaycock and Parfitt 1981) with further application of methods of statistical thermodynamics of irreversible processes (Kreuzer and Payne 1988b) and experimental data on pair correlation function (Flood 1967). 

Figure B3.2.1. The band structure of hexagonal GaN, calculated using EHT-TB parameters detemiined by a genetic algorithm [23]. The target energies are indicated by crosses. The target band structure has been calculated with an ab initio pseudopotential method using a quasiparticle approach to include many-particle corrections [194].

Development of methods related to DFT that can treat this situation accurately is an active area of research where considerable progress is being made. Two representative examples of this kind of work are P. Rinke, A. Qteish, J. Neugebauer, and M. Scheffler, Exciting Prospects for Solids Exact Exchange Based Functional Meet Quasiparticle Energy Calculations, Phys. Stat. Sol. 245 (2008), 929, and J. Uddin, J. E. Peralta, and G. E. Scuseria, Density Functional Theory Study of Bulk Platinum Monoxide, Phys. Rev. B, 71 (2005), 155112. 

Further we present the results of our calculations of the Li- ike iGplasma satellite lines on the basis of QED PT with ab initio zeroth-order approximation for three-quasiparticle systems, together with the optimized Dirac-Fock results and experimental data for comparison. In Table 4 there are displayed the experimental value (A) for wavelength (in A) of the Ti-like lines dielectron satellites to the ls So-ls3p Pi line of radiation in the K plasma, and the corresponding theoretical results (B) PT on 1/Z (C) QED PT (our data) (D) calculation by the AUTOJOLS method, and (E) MCDF [12, 21],... 

Figure 5. Quasiparticles density of states obtained from Gutzwiller method for Plutonium in S phase.

But this phase factor can be selected so that the signs of the CFP for almost filled shells are the same as in the quasispin method. It is worth recalling here that finite transformations generated by quasispin operators define the passage to quasiparticles. In much the same way, in the quasispin space of a shell of equivalent electrons the unitary transformations... 

That allows us to extract from the JFF experiment both components of quasiparticle conductivity oc and oab and their temperature dependences [17] (Fig. 10). As shown, they both are consistent with those measured by other independent methods. 

This hierarchy of approximations constitutes a guide for judging the quality of the methods discussed below that aim to improve the efficiency of quasiparticle electron propagator calculations. 

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. 

Comparison of this conclusion with the ordering given in the introduction indicates that there are now many more options for the calculation of EADEs with quasiparticle electron propagator methods. Furthermore, the accuracy gap between EP2 and P3 or OVGF methods has been filled and better compromises for accuracy and computer resources are available for large molecules. In particular, the QVOS... 

One-particle spectral properties of a Luttinger liquid. The absence of quasiparticles in a Luttinger liquid is also manifest in the one-particle spectral properties. As we have seen in the framework of the ID renormalization group method in the gapless case, there is a power-law decay of the one-particle spectral weight at the Fermi level. This power law behavior is also confirmed in the framework of the bosonization technique [146, 147], namely... 

Quasiparticle calculations on nucleic acid fragments with one or two bases yield many final states that may be obtained from anionic states by electron detachment. The QVOS procedure introduces only minor errors while providing large improvements in computational efficiency. Propagator calculations on an anion with two thymine bases amend the order of final states predicted by Hartree-Fock orbital energies and exhibit the need for correlated methods in interpreting anion photoelectron spectra of nucleic acid fragments. 

Role of quantum statistics. When considering complex systems by methods of statistical physics, one operates with their time-dependent distributions. In fermionic systems (see Yu. Ozhigov), statistical requirements imply that we must replace the independent-particle description by a quasiparticle formalism for quantum information processing. Effects of statistical fluctuations on coherent scattering processes (see M. Blaauboer et al.) suggest the need for furher exploration of the role of statistics on the dynamics of entangled systems. 

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