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1
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1842624342
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edited by, G. Bergmann, Y. Bruynseraede, B. Kramer, Springer, Berlin
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(1985)
Localization, Interaction and Transport Phenomena in Impure Metals
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Webb, R.A.1
Washburn, S.2
Umbach, C.P.3
Laibowitz, R.B.4
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32
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84931506805
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The arguments which predict large statistical fluctuations in g for a fixed energy, E, are typically derived by excluding configurations for which E is an eigenvalue. Thus the large fluctuations in g arise from small fluctuations in ln g (or equivalently, the inverse localization length) from configuration to configuration; the fluctuations in g versus E in a given sample seem to be primarily due to resonances and not due to fluctuations in the inverse localization length as a function of energy away from a resonance. Therefore it is not at all clear that g(E) in the strongly-localized regime will have identical fluctuations as those from sample to sample, although both are certainly expected to have large fluctuations. As noted later, the physical basis for our ergodic hypothesis relating magnetic field fluctuations to statistical fluctuations may also break down in the strongly-localized regime, so the apparent validity of our ergodic hypothesis in the metallic regime is not trivial.
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58
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84931506803
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The energy interval over which the spectrum exhibits spectral rigidity is just Ec =hD/L2, the energy correlation range derived in Refs. 13, 47, and 59, as discussed in the text.
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75
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84931506807
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Although there is a systematic perturbation expansion for g in the small parameter (kF l)-1, the coefficients in that expansion are divergent for d <= 2. This observation was an important justification of the result implied by the scaling theory of localization that all states are localized for any degree of disorder in these dimensions (see Ref. 29).
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93
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84931506790
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In fact, early numerical studies of the scaling of the average conductance with size near the metal-insulator transition gave size-independent error bars from which the magnitude of the universal conductance fluctuations can be obtained (see Ref. 56).
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99
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18844430323
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l app 1 and hence, while correct, In Ref. 44 it was incorrectly stated that the rms change induced by moving a single strong scatterer in two dimensions would be of order e2 /h for any metal, independent of disorder. The effect is indeed size independent in two dimensions, but decreases with decreasing disorder in the manner stated in the text. The numerical calculations done to confirm the analytic results in Ref. 44 were done for kF, did not reveal the error. More detailed corrections are given in an erratum
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(1986)
Phys. Rev. Lett.
, vol.56
, pp. 2772E
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