Complex quasiparticle

This kind of semi-phenomenological theory is unsatisfactory from at least two points of view (1) No theory exists for the tunnel matrix elements that would take the complex quasiparticle structure on both sides in account and (2) the order parameter near the physical barrier behaves inhomogenously so that - if the corresponding regions are not formally included into the barrier - only the semiclassical theory of superconductivity appears appropriate (Ashauer et al. 1986). Furthermore, for reliable estimates of the size of tunnel currents, the orientation of interfaces relative to the crystal axes (Geshkenbein and Larkin 1986) and the influence of inhomogeneity on the spin-orbit coupling (Fenton 1985) may have to be taken properly into account. 

As a second example, we compare in O Table 24-2 first-order transitions calculated using the hybrid TPSSh and HSE functionals (Barone et al. 2005a), and calculations considering GW plus electron-hole interactions (GW + e-h) (Spataru et al. 2008), with experimental values. Here, it is worth to point out the results obtained with hybrid functionals, that predict peak positions in agreement with more complex quasiparticle and excitonic effects approaches. An explanation for this behavior has been recently presented by Brothers et al. (2008). 

That is precisely which is reported say in [123] on example of Pd complexes (and for other systems in Ref. [124]) the TDDFT excitation energies are systematically lower than the experimental ones. In this context it becomes clear that the TDDFT may be quite useful for obtaining the excitation energies in those cases when the ground state is well separated from the lower excited states and can be reasonably represented by a single determinant wave function may be for somehow renormalized quasiparticles interacting according to some effective law, but shall definitely fail when such a (basically the Fermi-liquid) picture is not valid. 

The complexity of our angular distribution spectra do not permit reliable extraction of mixing ratios for the I+I-l transitions in the Trgg 2 band. Assuming that these are pure Ml, a 10 fold increase in the experimental B(M1)/B(E2) is observed between the one and three quasiparticle bands. 

The Scatchard model23,24 is perhaps the best-known quasiparticle description of complexation by humic substances. The quasiparticles in this case are hypothetical polymeric molecules bearing one class of functional group that forms a 1 1 complex with a cation. The conditional stability constant for the complexation of 1 mol of a metal by 1 mol of a given class of Scatchard quasiparticles can be expressed as... 

Fig. 2.7. Logical flowchart relating several quasiparticle models of metal complexation reactions.

In addition to its relative simplicity, the quasiparticle approach has the advantage of a formal mathematical structure that is analogous to that described in Section 2.1 for complexes involving nonpolymeric ligands, such as F or C2O4. Thus, for example, the complexation reaction between Al3+ and a humic substance Scatchard quasiparticle, L, can be written by analogy with Eq. 2.5a ... 

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. 

In the preceding section it was shown that the formation of bound states of phonons leads to the appearance of a new type of resonance of the dielectric tensor ij(co). It is clear, of course (23), that the nonlinear polarizabilities should have analogous resonances, and this also concerns, besides biphonons, other types of bound states of quasiparticles, such as biexcitons, electron-exciton complexes, etc. 

However, in a realistic situation some dissipation processes are involved and the dielectric tensor becomes complex. Then, generally speaking, both the energy and the wavevector have to be considered as complex variables u> = ui + iw", q = q I q". Nevertheless, the picture of quasiparticles is still applicable if u>" -C uj and q" -C " is small in comparison with the quasiparticle energy and second, the uncertainty of the wavevector 5q = q" is small in comparison with the wavevector. 

Other known methods that have been used in the study of lanthanides include the OP scheme, the LDA + U approach, where U is the on-site Hubbard repulsion, and the DMFT, being the most recent and also the most advanced development. In particular, when combined with LDA + U, the so-called LDA - - DMFT scheme, it has been rather successful for many complex systems. We note here that both DMFT and LDA + U focus mostly on spectroscopies and excited states (quasiparticles), expressed via the spectral DOS. In a recent review article (Held, 2007), the application of the LDA + DMFT to volume collapse in Ce was discussed. Finally, the GW approximation and method, based on an electron self-energy obtained by calculating the lowest order diagram in the dynamically screened Coulomb interaction, aims mainly at an improved description of excitations, and its most successful applications have been for weakly correlated systems. However, recently, there have been applications of the quasi-particle self-consistent GW method to localized 4f systems (Chantis et al., 2007). 

If there are many valence protons and neutrons present in the nucleus, traditional shell model calculations lead to insurmountable difficulties. Fortunately, the Bardeen-Cooper-Schrieffer (BCS) theory provides a good approximation method to the seniority-zero shell model, and allows to describe very complex nuclei, too. In the BCS quasiparticle calculations long chains of nuclei can be treated in a relatively simple way. The method was first applied in the theory of superconductivity by Bardeen et al. (1957), then used for nuclear physics by Bohr et al. (1958), Soloviev (1958), and Belyaev (1959). The quasiparticle concept was introduced into nuclear physics by Valatin (1958) and Bogoliubov (1958). The theory is explained in detail in several textbooks (Lawson 1980 Ring and Schuck 1980 Soloviev 1981 Heyde 1990 Nilsson and Ragnarsson 1995 Fenyes 2002). 

We have seen that many-body-based methods provide an ab-initio way to treat the Coulomb correlation in an N electron system without the expensive cost of QMC calculations. However, they are computationally more demanding than routine LDA-KS calculations and, hence, the feasibility of their application to complex systems is unclear, especially in the context of ab-initio molecular dynamics calculations, where many total-energy evaluations are required. As described in Sect. 5.3, the main problem when constructing approximations to E c [n] is related to its inherent non-analytical character which is due to the specific way in which the KS mapping between the real and the fictitious systems is done. However, this is not the only possible realisation of DFT and recently, new DFT methods have been proposed [112,113]. In these generalised Kohn-Sham schemes (GKS) the actual electron system is mapped onto a fictitious one in which particles move in an effective non-local potential. As a result of this, it is possible to describe structmal properties at the same (or better) level than LDA/GGA but improving on its description of quasiparticle properties. 

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