Distortion field-induced

A brief review is given on electronic properties of carbon nanotubes, in particular those in magnetic fields, mainly from a theoretical point of view. The topics include a giant Aharonov-Bohm effect on the band gap and optical absorption spectra, a magnetic-field induced lattice distortion and a magnetisation and susceptibility of ensembles, calculated based on a k p scheme. 

The situation changes drastically in the presence of a high magnetic field perpendicular to the axis. As has been discussed in Sec. 2, Landau levels without dispersion appear at the Fermi level considerably, leading to a magnetic-field induced distortion [13,14]. 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

The concerns we have expressed are bound to get even more acute if the problem under study demands that we are able to adequately describe distortion effects induced in the electron distribution by external fields. The evaluation of linear (and, still more, non linear) response funetions [1] by perturbation theory then forces one to take care also of the nonoccupied portion of the complete orbital spectrum, which is entrusted with the role of representing the polarization caused by the external fields in the unperturbed electron distribution [4], ... 

Besides the collision-induced dipoles, we will occasionally refer to field-induced dipoles, or to rotation-induced dipoles, that is dipoles induced by an external electric field, or by centrifugal forces distorting certain symmetries of rotating molecules. Moreover, we will be interested in the dipoles induced in binary, ternary, etc., systems as we proceed. 

A CDW is a periodic modulation of the conduction electron density within a material. It is brought about when an applied electric field induces a symmetry-lowering lattice modulation in which the ions cluster periodically. The modulation mechanism involves the coupling of degenerate electron states to a vibrational normal mode of the atom chain, which causes a concomitant modulation in the electron density that lowers the total electronic energy. In one-dimensional systems, this is the classic Peierls distortion (Peierls, 1930, 1955). It is analogous to the JT distortion observed in molecules. 

Henry s calculations are based on the assumption that the external field can be superimposed on the field due to the particle, and hence it can only be applied for low potentials (f < 25 mV). It also does not take into account the distortion of the field induced by the movement of the particle (relaxation effect). Wiersema, Loeb and Overbeek [19] introduced two corrections for the Henry s treatment, namely the relaxation and retardation (movement of the hquid with the double layer ions) effects. A numerical tabulation of the relationship between mobility and zeta-potential has been provided by Ottewill and Shaw [20]. Such tables are useful for converting u to f at aU practical values of kR. 

Probing on the separation of incident and reflected waves, a concern still remains two field quantities must be determined on the source plane and updated interactively. For waveguide discontinuities, the regularly implemented scheme of the third case places the source and the near-end terminal plane at the same position, inserts the excitation, and then applies the ABC to the source plane after the pulse has been fully propagated. Nonetheless, before any truncation process is allowed to initiate, DC distortions are induced near the incident waveform by the electric and magnetic boundary conditions. This is another reason why usual techniques cannot be located very close to the discontinuity. An efficient way to alleviate the prior weakness is to... 

An early survey of the possible sources for the hypersensitivity concluded that the most likely candidate was a mechanism based on the inhomogeneities of the dielectric surrounding the rare-earth or actinide ion (4). It runs as follows. The radiation field induces sinusoidally fluctuating dipole moments in the ligands surrounding the ion. These induced dipoles necessarily radiate, and the emitted fields impinge on the rare-earth or actinide ion. Because of the proximity of source and receiver, the plane-wave condition no longer applies the wave fronts are sufficiently distorted to produce substantial quadrupole components. 

In addition to orienting dipoles, electric fields induce dipole moments in molecules, since electrons and nuclei experience forces in opposite directions in the same electric field and since electrons, being less massive, move much more easily than nuclei in a field. The quantity that measures the ease with which the electron cloud in a certain molecule can be distorted is the molecular polarizability ccq. The magnitude of an induced dipole is given as... 

For example. Fig. 2 shows a SchHeren texture, which is typical of nematic distortions of the director field (visible as dark branches usually named brushes). These distortions are induced by the perpendicular anchoring on the microscope slide of topological defects, called disclination lines, which are numbered from 1 to 7 in Fig. 2. These disclination lines can be classified into two groups according to their local topology as the dark brushes seen around these defects can rotate either clockwise or counterclockwise as the crossed polarizers are rotated simultaneously while the sample is kept fixed. This is due to the two different possible defect topologies illustrated in Fig. 2 for cases 1 and 2 [1]. 

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