Electron gas, system

There is, however, another type of transition possible in two dimensions, a transition between states without LRO. This is the Kosterlitz-Thouless transition [8] mentioned in Sections II and V.B.l. It is relevant to superconductivity, commensurate-incommensurate transitions [61], planar magnetism, the electron gas system, and to many other systems in two dimensions. It involves vortices (thus the requirement of a two-component order parameter) characterized by a winding number q = (1/2-rr) dr V0, in which 0 is the phase of the order parameter (see also Ref. 4), the amplitude being fixed. These free vortices have an energy [see Eq. (28)] given by... 

T. J. Raecker and A. E. DePristo, Int. Rev Phys. Chem., 93, (1991). Theory of Chemical Bonding Based on the Homogeneous Electron Gas System. 

Polymer-nanocomposites with semiconductor nanoparticles possess a number of unique features which attracted much attention from physicists and chemists in the early 1980s [17-19]. Nanoparticles of semiconductors in a polymer matrix are extremely interesting to physicists since they exhibit behavior typical for one-dimensional electron gas systems with effects such as quantum confinement, discretization of the energy spectrum, unique non-linear optical properties, etc. 

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

X-Ray structural data and recent high level theoretical calculations confirm that this neutral, diamagnetic dithiadiazole is an aromatic six k-electron ring system. The gas-phase infra-red and photoelectron spectra of S2N2CO have also been reported. ... 

Early attempts at deducing functionals for the kinetic and exchange energies considered a non-interacting uniform electron gas. For such a system it may be shown that T[p] and K[p] are given as... 

The existence of the first HK theorem is quite surprising since electron-electron repulsion is a two-electron phenomenon and the electron density depends only on one set of electronic coordinates. Unfortunately, the universal functional is unknown and a plethora of different forms have been suggested that have been inspired by model systems such as the uniform or weakly inhomogeneous electron gas, the helium atom, or simply in an ad hoc way. A recent review describes the major classes of presently used density functionals [10]. 

At the center of the approach taken by Thomas and Fermi is a quantum statistical model of electrons which, in its original formulation, takes into account only the kinetic energy while treating the nuclear-electron and electron-electron contributions in a completely classical way. In their model Thomas and Fermi arrive at the following, very simple expression for the kinetic energy based on the uniform electron gas, a fictitious model system of constant electron density (more information on the uniform electron gas will be given in Section 6.4) ... 

In this section we introduce the model system on which virtually all approximate exchange-correlation functionals are based. At the center of this model is the idea of a hypothetical uniform electron gas. This is a system in which electrons move on a positive background charge distribution such that the total ensemble is electrically neutral. The number of elec-... 

This is a very drastic approximation since, after all, the density in our actual system is certainly anything but constant and does not even come close to the situation characteristic of the uniform electron gas. As a consequence, one might wonder whether results obtained with such a crude model will be of any value at all. Somewhat surprisingly then, experience tells us that the local (spin) density approximation is actually not that bad, but rather deliv-... 

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