Critical Conductance of a Mesoscopic System: Interplay of the Spectral and Eigenfunction Correlations at the Metal-Insulator Transition

Abstract

We study the system-size dependence of the averaged critical conductance $g(L)$ at the Anderson transition. We have: (i) related the correction $δg(L)=g(\infty)-g(L)\propto L^{-y}$ to the spectral correlations; (ii) expressed $δg(L)$ in terms of the quantum return probability; (iii) argued that $y=η$ -- the critical exponent of eigenfunction correlations. Experimental implications are discussed.