Quasi-particle model

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. 

Barat, M. (1976) The Quasi-Molecular Model in Heavy Particle Collisions, in F. J. Wuilleumier (ed.), Photoionization and other probes of many-electron interactions, Plenum Publishing Corporation, New York, pp. 229-253. 

In the above, we have repeatedly mentioned the bound of applicability of the BCS theory. It means more specifically that the BCS theory is to be used only when the (effective) space size and the particle number n, are both sufficiently larger than is the quasi-particle number (which is the senioprity v in the Ginocchio model). 

To cover the gap between them the Hubbard model Hamiltonian was quite generally accepted. This Hamiltonian apparently has the ability of mimicking the whole spectrum, from the free quasi-particle domain, at U=0, to the strongly correlated one, at U —> oo, where, for half-filled band systems, it renormalizes to the Heisenberg Hamiltonian, via Degenerate Perturbation Theory. Thence, the Heisenberg Hamiltonian was assumed to be acceptable only for rather small t/U values. 

The discussion of the parity operator can now be repeated verbatim with states, replaced by the molecular states ,, and the understanding that the set, are associated with the quasi-particle solutions of the quantum field theory of the chiral medium. In the next section we discuss some models of these molecular (quasi-particle) states. 

The above formulation is quite general and applies equally well to quasi-complete model spaces having m holes and n partic 1es.When there are several p-h valence ranks in the parent model space, the situation is fairly complicated. The subduced model spaces in this case may belong to the parent model space itself. The valence-universality of ft in such a situation implies that ft is the wave—operator for all the subduced model spaces, in addition to those which have same number of electrons as in the parent model space. It appears that a more convenient route to solve this problem is to redefine the core in such a way that holes for the problem become particles and treat it as an IMS involving valence particles only. 

The interpretation of the interband transition is based on a single particle model, although in the final state two particles, an electron and a hole, exist. In some semiconductors, however, a quasi one-particle state, an exciton, is formed upon excitation [23,24]. Such an exciton represents a bound state, formed by an electron and a hole, as a result of their Coulomb attraction, i.e. it is a neutral quasi-particle, which can move through the crystal. Its energy state is close to the conduction band (transition 3 in Fig. 2), and it can be split into an independent electron and a hole by thermal excitation. Therefore, usually... 

In order to study the decoherence of quasi-particles within BEC, we use Bragg spectroscopy and Monte Carlo hydrodynamic simulations of the system [Castin 1996], and confirm recent theoretical predictions of the identical particle collision cross-section within a Bose-Einstein condensate. We use computerized tomography [Ozeri 2002] of the experimental images in determining the exact distributions. We then conduct both quantum mechanical and hydrodynamic simulation of the expansion dynamics, to model the distribution of the atoms, and compare theory and experiment [Katz 2002] (see Fig. 2). 

Few studies have been made on transport processes involving concentrated solutions. In the concentrated solutions, in the range of dehydrated melt formation, incompletely hydrated melts and anhydrous salt melts, various structural models are described to define their properties, i.e. the free-volume model, the lattice-model and the quasi-crystalline model. Measured and calculated transport phenomena do not always represent simple ion migration of individual particles, but instead we sometimes find them to be complicated cooperative effects (27). 

Beginning less than 10 years ago, the independent-particle model for atoms was challenged, first for a specific set of rather exotic states of helium and, more recently, for the ground and ordinary excited states of the alkaline earth atoms Be, Mg, Ca, Sr, and Ba. Evidence has been building that the quantization in these two-electron and quasi-two-electron atoms corresponds to collective, moleculelike behavior, rather than to independent-particle-like behavior. 

In practice, a solid catalyst is most conveniently modeled as a quasi-homo-geneous phase. Even if the catalyst particle is porous, visualize it as a homogeneous, but permeable solid. Mass transfer in its interior is retarded by two effects obstruction of part of the cross-sectional area by the solid material, and diffusion paths that are longer because molecules have to wind their way around the obstructions (tortuosity effect). In the quasi-homogeneous model, the retardation is accounted for by the use of appropriately smaller "effective mass-transfer or diffusion coefficients. 

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