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By Sergei Baranovski

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23) determines conductance of the system as a function of its size L and the position of the Fermi level. 26) the most divergent terms as g → 0 and g0 → ∞, we may write [48] ln ln (( g1 + g ) g ) + π 2 g0 + ϕ ( g, g0 ) = ln ( L l ). 25) as g → 0 and g0 → ∞. 26) a ( g, g0 ) = exp [π 2 g0 + ϕ ( g, g0 )]l. 27) where CHARGE TRANSPORT VIA DELOCALIZED STATES 21 For small g, the quantity a (g, g0) does not depend on g and becomes equal to the localization radius of strongly localized states. Generally, the function a (g, g0) is the localization length that characterizes the rate of conductance decay with increasing L.

3h ¯ /t. 23) determines conductance of the system as a function of its size L and the position of the Fermi level. 26) the most divergent terms as g → 0 and g0 → ∞, we may write [48] ln ln (( g1 + g ) g ) + π 2 g0 + ϕ ( g, g0 ) = ln ( L l ). 25) as g → 0 and g0 → ∞. 26) a ( g, g0 ) = exp [π 2 g0 + ϕ ( g, g0 )]l. 27) where CHARGE TRANSPORT VIA DELOCALIZED STATES 21 For small g, the quantity a (g, g0) does not depend on g and becomes equal to the localization radius of strongly localized states. Generally, the function a (g, g0) is the localization length that characterizes the rate of conductance decay with increasing L.

3), we see that d = 2 is the critical dimensionality for the problem in question, and the localization properties of electronic states in systems with d < 2 and d > 2 are different. Indeed, for a system of size L >> l and extended electron states, one can define conductivity, independent of L. , the tendency to localization is realized, whereas for d > 2, the quantity z /w increases with the system size. , of the localization properties, can be performed using the assumption of scaling invariance.

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