Dynamical conductivity and localization corrections in small and large quantum dots and disordered systems

Localization effect on the dynamical conductivity σ(ω) is examined in quantum dots and disordered electron systems. For the small volume limit, which is well described by the random matrix theory, Re[σ(ω)] is known to be proportional to the DOS correlator 〈ν(E)ν(E+ω)〉, hence to the universal two-level correlator R2WD(ω/Δ). Looking at localization effect, however, reveals the discrepancy between Re[σ(ω)] and 〈ν(E)ν(E+ω)〉, because only the former, not the latter, is consistent with the logarithmic weak localization correction in 2D and its RG treatment. We investigate and clarify the issue by evaluating the linear response σ(ω) directly from the nonlinear sigma formulation.