One-dimensional electron gas

Quantitative MO-LCAO calculations as well as treatments as a one dimensional electron gas have been advanced. Special parameters, however, have to be introduced to account for different end groups and branching of the rr-system. Empirically a linear correlation between and n is verified in all cases so far investigated. That is, violenes behave like cyanines. The vinylene shift amounts to 100—150 nm in contrast to that of the corresponding forms OX and RED with 20-40 mm ... 

Figure 14 shows some examples. An interesting point is that all modes are localized [105], as one expects from the quantum-mechanical analog of a one-dimensional electron gas in a random potential [157]. Alternatively, from a localized tight-binding point of view, micromagnetic delocalization... 

If one puts two electrons per quantum state ("spin-up and spin-down"), then the minimum resistance becomes 2R0 = 25.812986 kQ. The internal resistance of a molecule has not yet been measured. Recently, it was shown that a degenerate quasi-one-dimensional electron gas in a GaAs GaAh YAsY system, when interrogated in a four-probe geometry, has zero resistance drop between probes 2 and 3, in contrast to the expected R0 between probes 1 and 4 the transport is ballistic [13]. 

It is obviously ideally suited to measuring the effect of the electron quantum fluctuations on the phonon frequency. What one immediately learns from Eq. (26) is that the propagator is quasistatic that is, the >m = 0 component dominates for T > co /2tt. This comes from the definition of the Matsubara frequencies for bosons [under Eq. (8)]. As far as the electrons are concerned, the atoms move very slowly (the adiabatic limit). If 2g2 gi> - g3 (see Fig. 5), the electrons are able to screen the slow lattice motion and thus soften the interactions. We are obviously interested in the 2kF phonons, which will be screened most effectively by the dominant 2kF charge response of the one-dimensional electron gas. 

Structural methods, p is obtained, with an accuracy of a few percent, through measurement of the critical wave vector of the structural instability accompanying the 2kF or 4kF instability of the one-dimensional electron gas. 

In quasi-one-dimensional conductors, the one-dimensional electron gas instability is responsible for the formation of a charge density wave (CDW) with wave vector 2kF and/or 4kF via electron-phonon coupling. Thus the measurement, in reciprocal wave vector units, of the corresponding 4 and 2kF scattering wave vectors gives the value and twice the value of the charge transfer p, respectively (e.g., see Ref. 114). 

However, as discussed extensively in review articles by Pouget [9] and by Barisic and Bjelis [10], the presence of both 2kF and 4kF anomalies, where kF is the Fermi wave vector of the quasi-one-dimensional electron gas, the fact that phonon softening at 2kF is relatively small, combined with theoretical considerations, have lead to the present-day viewpoint that electron-electron Coulomb interactions play an important role. 

Spin and charge excitations are thus decoupled by coulombic interactions in the one-dimensional electron gas. However, the one-dimensional Fermion system is not a Fermi liquid, as indicated by the behavior of the momentum distribution function, which does not exhibit a Fermi step at kF and presents a single-particle density of states vanishing according to a power law singularity at EF. This is a Luttinger liquid [29] with... 

It is possible to exactly identify and characterize the radical species and chain structures of the reaction intermediates, which are determined by their different reactive or unreactive chain ends. The reactive intermediates are best described by diradical (DR), asymmetric carbene (AC) and dicarbene (DC) oligomer molecules of different lengths. The respective singlet (S = 0), triplet (S = I) or quintet (S = 1) states and their roles in the polymerization process are investigated in detail by solid state spectroscopy. A one-dimensional electron gas model is successfully applied to the optical absorption series of the DR and AC intermediates as well as on the different stable oligomer SO molecules obtained after final chain termination reactions. 

Table 3. Data used in the one-dimensional electron gas model calculation following Eq. (2)...

Cramer S in his studies of the iodine inclusion compounds considers that in some cases the iodine chains can be represented as a one-dimensional electron gas. From the position of the light absorption maxim un (6200 A.) together with one-dimensional Fourier analyses of the iodine gas, Cramer concludes that there are perhaps 14 or more iodine atoms, spaced with an I—I distance of 3.06 A. in a polyiodide ion. 

M. A. Stroscio, Interaction between longitudinal-optical phonon modes of a rectangular quantum wire with charge carriers of a one-dimensional electron gas, Phys. Rev. B, 40, 6428-6432 (1989). 

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. 

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