Anderson localisation

The quantum mechanics of classically diffusive systems has been studied mainly in the context of Anderson localisation and localisation-delocalisation transitions, see e.g. Dittrich (1996) and Janssen (1998) for recent review articles. 

For g values less than about 0.3 Mott suggests that Anderson localisation occurs. The conductivity arises from the thermal excitation of carriers across the mobility gap or by hopping processes. The semi-empirical relationship for the conductivity in this regime (Stuke (1969)) is... 

Johnston, R.N., Shaw, C., Halton, D.W., Verhaert, P., Blair, K.F., Brennan, G.P., Price, D.A. and Anderson, P.A.V. (1996) Isolation, localisation, and bioactivity of the FMRFamide-related neuropeptides GYlRFamide and YIRFamide from the marine turbel larian Bdelloura Candida. Journal of Neurochemistry 67, 81 4-821. 

Rice, J. R., Papastephanou, C., and Anderson, D. G., Isolation, localisation and biosynthesis of crassin acetate in Pseudoplexaura porosa (Houttyun), Biol. Bull., 138, 334, 1970. 

Anderson, D. G., Gorgosterol biosynthesis localisation of squalene formation in the zooxanthellar component of various gorgonians, Comp. Biochem. Physiol., 81B, 423, 1985. 

In a semiconductor, as discussed in the previous section, localisation can also occur as the width of the allowed energy band is reduced, and this was defined in terms of a limiting mobility. The Anderson model shows that disorder can lead to localisation in metals as well as semiconductors. In metals, since conduction is due only to electrons within a partially filled band, the energy in the band tail that separates localised from delocalised electron states is termed the mobility edge. The onset of localisation in a metal occurs at a minimum conductivity. This can be seen as follows. For an electron at the Fermi energy its mean free path, l, is just the scattering time, r, multiplied by the electron velocity at the Fermi energy, vF. Then, from Equations (4.1) and (4.2) it follows that ... 

Tian, Q., Streuli, M., Saito, H., Schlossman, J.F. and Anderson, P. (1991). A polyadenylate binding protein localised to the granules of cytolytic lymphocytes induces DNA fiagmentation in target cells. Cell 67, 629-639. 

In this sense, atomic multiplet theory provides complementary information about the valence state. One can take the view that this information should be used, and then blended in some way with the conceptual framework of the Anderson single-impurity model, so that the matrix elements coupling the / electrons to the conduction band can continue to play the decisive role in determining the extent of / electron localisation. 

There have been several attempts to combine information from atomic physics with the Anderson impurity scheme outlined above, so as to calculate multiplet structure consistently with the occurrence of hybridisation. Prom the atomic physics standpoint, the possibility of correcting for the loss of localised 4/-electron density by reducing the Slater-Condon integrals by 10 or 20% respectively, depending on whether one or two 4/ electrons are involved, has been suggested [620]. The precise amount of the correction required is of course borrowed from parametric studies, because atomic physics per se can yield no information whatever on the reduction of charge density due to hybridisation. This is the reverse path to the one outlined above, i.e. it feeds back information from the parar metric studies into atomic calculations, whose ab initio character must of course be sacrificed. 

All the lightning conductors should be periodically tested, to see that they are in working condition, at least every three months, according to Mr Richard Anderson. The object of the test is to determine the resistance of the earth-connection, and to localise any defective joints or parts in the conductors. The best system of testing the conductors is to balance the resistance of each of the earths against the remainder of the system, from... 

Anderson et al. have presented solid-state NMR analysis of local structural environments in phosphate glasses for educational purposes. " In particular, the solid-state NMR wide-line spectra of a series of sodium phosphate glasses have been considered, which can also be simulated by spectral addition of reference solid-state spectra obtained for pure pyrophosphate and metaphosphate salts. The example chosen introduces the principles of solid-state NMR and allows interpretation of the spectrum in terms of the composition and localised phosphate environment. 

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