scaling theory of Anderson localization

Question

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian

$$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$

His question was whether the eigenstates are localized or extended. But in the paper by the 'Gang of Four', the four introduced the dimensionless conductance

$$ g(L) = \frac{2 \hbar}{e^2} G(L) . $$

And it seems that this quantity plays an central role.

But how is this quantity related to the original problem of Anderson? How is it related to the localization/delocalization of the eigenstates?

Is $g(L)$ determined by the Hamiltonian above, or some more parameters are needed, say, the temperature?

This post imported from StackExchange Physics at 2015-02-12 10:59 (UTC), posted by SE-user kaiser