Self-energy model

Representing a heteropolymer, the model tries to capture tliree contributions to the overall energy E of each conformation the self-energy e of each amino acid, a bond energy tenn Ji i+i between two neighboring residues, and a nonbonded Ki j interaction... 

The physical meaning of our final equation is best seen on eqn 39. The term containing w is essentially the self-energy correction introduced by Mulliken in his analysis of electronegativities to account for the average repulsion of electrons occupying the same orbital. In order to get an idea of the orders of magnitude, let us apply eqn 39 to a model computation of FeCO, made to compare the ClPSl results of Berthier et al. [11] with those of a simple orbital scheme. Consider one of the two x systems of FeCO, treated under the assumption of full localization (and therefore strict cr — x separation)... 

In this contribution we will deal with electron-electron correlation in solids and how to learn about these by means of inelastic X-ray scattering both in the regime of small and large momentum transfer. We will compare the predictions of simple models (free electron gas, jellium model) and more sophisticated ones (calculations using the self-energy influenced spectral weight function) to experimental results. In a last step, lattice effects will be included in the theoretical treatment. 

The Drude oscillators are typically treated as isotropic on the atomic level. However, it is possible to extend the model to include atom-based anisotropic polarizability. When anisotropy is included, the harmonic self-energy of the Drude oscillators becomes... 

A description of nuclear matter as an ideal mixture of protons and neutrons, possibly in (5 equilibrium with electrons and neutrinos, is not sufficient to give a realistic description of dense matter. The account of the interaction between the nucleons can be performed in different ways. For instance we have effective nucleon-nucleon interactions, which reproduce empirical two-nucleon data, e.g. the PARIS and the BONN potential. On the other hand we have effective interactions like the Skyrme interaction, which are able to reproduce nuclear data within the mean-field approximation. The most advanced description is given by the Walecka model, which is based on a relativistic Lagrangian and models the nucleon-nucleon interactions by coupling to effective meson fields. Within the relativistic mean-field approximation, quasi-particles are introduced, which can be parameterized by a self-energy shift and an effective mass. 

Phenomenological quasiparticle model. Taking into account only the dominant contributions in (7), namely the quasiparticle contributions of the transverse gluons as well as the quark particle-excitations for Nj / 0, we arrive at the quasiparticle model [8], The dispersion relations can be even further simplified by their form at hard momenta, u2 h2 -rnf, where m.t gT are the asymptotic masses. With this approximation of the self-energies, the pressure reads in analogy to the scalar case... 

In this section, we describe our model, and give a brief, self-contained account on the equations of the non-equilibrium Green function formalism. This is closely related to the electron and particle-hole propagators, which have been at the heart of Jens electronic structure research [7,8]. For more detailed and more general analysis, see some of the many excellent references [9-15]. We restrict ourselves to the study of stationary transport, and work in energy representation. We assume the existence of a well-defined self-energy. The aim is to solve the Dyson and the Keldysh equations for the electronic Green functions ... 

These studies were with polycrystalline copper, but more detailed results (Fig. 9) were obtained subsequently (44) with Cu(100), Cu(l 11), and Cu(l 10) surfaces XPS, UPS, LEED, and mass spectrometric data being combined to provide a self-consistent model. The surface species formed with their associated N(ls) and 0(ls) binding energies (eV) on exposing copper surfaces to NO(g) are listed in Table I. 

Spiering et al. (1982) have developed a model where the high-spin and low-spin states of the complex are treated as hard spheres of volume and respectively and the crystal is taken as an isotropic elastic medium characterized by bulk modulus and Poisson constant. The complex is regarded as an inelastic inclusion embedded in spherical volume V. The decrease in the elastic self-energy of the incompressible sphere in an expanding crystal leads to a deviation of the high-spin fraction from the Boltzmann population. Pressure and temperature effects on spin-state transitions in Fe(II) complexes have been explained based on such models (Usha et al., 1985). 

It is not possible for conventional electromagnetic models of the electron to explain the observed property of a point charge with an excessively small radial dimension [20]. Nor does the divergence in self-energy of a point charge vanish in quantum field theory where the process of renormalization has been applied to solve the problem. 

The subscripts i which have been added refer to the different species of ion-dipoles, and the symbols ax(D),... indicate that the respective coefficients have to be calculated with the value of D and n2. From the way our work function A has been derived, it is evident that it contains the contributions which are caused by the presence of the solutes and by the change in dielectric constant of the solvent. The contributions which result from the first term in Equation 19 and which represent the work which is required to build up the ion-dipole in a standard environment (e.g., a vacuum) have disappeared from Equation 24 (being identical in A and A o). This self-energy of the particles is without interest for the present investigation and depends, of course, in a decisive way on the underlying model. 

The most drastic effect on the losses of the thermal energy is due to dissociation of molecular hydrogen. According to Fox and Wood (1985) as much as a half of the thermal energy behind the shock front is absorbed due to dissociation of Hg molecules. At the same time photodissociation of Hg molecules in the precursor causes retardation of the collisional ionization in the relaxation zone, whereas the precursor structure is very sensitive to the radiation flowing from the wake (Gillet and Lafon 1983 1984). So, the self-consistent model of the radiative shock is urgently needed. 

It will be useful to express the self-energy of the polaron in the two models in units of a dimensionless coupling constant which is considerably important in polaron theory ... 

The aim of this work is to demonstrate that the above-mentioned unusual properties of cuprates can be interpreted in the framework of the t-J model of a Cu-O plane which is a common structure element of these crystals. The model was shown to describe correctly the low-energy part of the spectrum of the realistic extended Hubbard model [4], To take proper account of strong electron correlations inherent in moderately doped cuprate perovskites the description in terms of Hubbard operators and Mori s projection operator technique [5] are used. The self-energy equations for hole and spin Green s functions obtained in this approach are self-consistently solved for the ranges of hole concentrations 0 < x < 0.16 and temperatures 2 K< T <1200 K. Lattices with 20x20 sites and larger are used. 

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