Semiclassical Analysis of the Conductance of Mesoscopic Systems

Abstract

The Kubo formula for the conductance of classically chaotic systems is analyzed semiclassically, yielding simple expressions for the mean and the variance of the quantum interference terms. In contrast to earlier work, here times longer than $O( \log \hbar^{-1} )$ give the dominant contributions, i.e. the limit $\hbar \rightarrow 0$ is not implied. For example, the result for the weak localization correction to the dimensionless conductance of a chain of $k$ classically ergodic scatterers connected in series is $-{1 \over 3} [ 1 - (k+1)^{-2} ]$, interpolating between the ergodic ($k = 1$) and the diffusive ($k \rightarrow \infty$) limits.