Quantum dots physical models

Clusters are intennediates bridging the properties of the atoms and the bulk. They can be viewed as novel molecules, but different from ordinary molecules, in that they can have various compositions and multiple shapes. Bare clusters are usually quite reactive and unstable against aggregation and have to be studied in vacuum or inert matrices. Interest in clusters comes from a wide range of fields. Clusters are used as models to investigate surface and bulk properties [2]. Since most catalysts are dispersed metal particles [3], isolated clusters provide ideal systems to understand catalytic mechanisms. The versatility of their shapes and compositions make clusters novel molecular systems to extend our concept of chemical bonding, stmcture and dynamics. Stable clusters or passivated clusters can be used as building blocks for new materials or new electronic devices [4] and this aspect has now led to a whole new direction of research into nanoparticles and quantum dots (see chapter C2.17). As the size of electronic devices approaches ever smaller dimensions [5], the new chemical and physical properties of clusters will be relevant to the future of the electronics industry. 

In mesoscopic physics, because the geometries can be controlled so well, and because the measurements are very accurate, current under different conditions can be appropriately measured and calculated. The models used for mesoscopic transport are the so-called Landauer/Imry/Buttiker elastic scattering model for current, correlated electronic structure schemes to deal with Coulomb blockade limit and Kondo regime transport, and charging algorithms to characterize the effects of electron populations on the quantum dots. These are often based on capacitance analyses (this is a matter of thinking style - most chemists do not consider capacitances when discussing molecular transport junctions). 

Many electron systems such as molecules and quantum dots show the complex phenomena of electron correlation caused by Coulomb interactions. These phenomena can be described to some extent by the Hubbard model [76]. This is a simple model that captures the main physics of the problem and admits an exact solution in some special cases [77]. To calculate the entanglement for electrons described by this model, we will use Zanardi s measure, which is given in Fock space as the von Neumann entropy [78]. 

In the previous section we have dealt with a simple, but nevertheless physically rich, model describing the interaction of an electronic level with some specific vibrational mode confined to the quantum dot. We have seen how to apply in this case the Keldysh non-equilibrium techniques described in Section III within the self-consistent Born and Migdal approximations. The latter are however appropriate for the weak coupling limit to the vibrational degrees of freedom. In the opposite case of strong coupling, different techniques must be applied. For equilibrium problems, unitary transformations combined with variational approaches can be used, in non-equilibrium only recently some attempts were made to deal with the problem. [139]... 

POWER-LAW BLINKING QUANTUM DOTS STOCHASTIC AND PHYSICAL MODELS... 

The harmonic oscillator is one of the most important and beautiful models in physics. When almost nothing is known, except that the particles ate held by forces, then the first model considered is the hannonic oscillator. This happened for the black body problem (discussed in Chapter 1), and now it is the case with the quantum dots, string theoiy," solvated electron," etc. 

FIG. 13 Herringbone order parameter and total energy for N2 (X model with Steele s corrugation). Quantum simulation, full line classical simulation, dotted line quasiharmonic theory, dashed line Feynman-Hibbs simulation, triangles. The lines are linear connections of the data. (Reprinted with permission from Ref. 95, Fig. 4. 1993, American Physical Society.)... 

The central teaching of the Lewis model is that the electrons are localized in the comers of a tetrahedron, where they are shared by two atoms. The Lewis model is, to a large extent, inconsistent with physical principles, since charged particles cannot be fixed in space, according to classical mechanics. However, the Lewis model may be justified on the basis of quantum mechanics. This is expressed in the natural bond orbital (NBO) model of Frank Weinhold. The MOs are also expressed in terms of hybridized AOs. The hybridized electron clouds replace the Lewis dots. In most cases, the NBO model shows that the time-independent wave function is in agreement with the Lewis model. 

Traditional models and theories for material properties and device operations assume that the physical quantities are described by continuous variables and are valid only for length larger than about 100 nanometers. When at least one dimension of a material structure is under this critical length, distinct behavior often emerges that cannot be explained by traditional models and theories. In the semiconductor device field, for instance, quantum effects (turmel effect, discrete energy levels...) appear when the active layer thickness is smaller than 10 nm. Reducing the dimensions of structures leads to entities, such as carbon nanotubes, quantum wires and dots, thin films, DNA-based structures, and laser emitters, which have unique properties. 

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