Semiclassical Analysis of the Conductance of Mesoscopic Systems

TL;DR

This paper uses semiclassical methods to analyze conductance in mesoscopic systems, revealing how quantum interference effects depend on classical chaos and extending understanding beyond the short-time regime.

Contribution

It provides a semiclassical framework for conductance that accounts for longer timescales, improving upon previous models limited to short-time approximations.

Findings

Derived simple expressions for mean and variance of interference terms.

Identified the dominant contributions from times longer than $O( ext log obreak \hbar^{-1} )$.

Calculated the weak localization correction for chains of ergodic scatterers.

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.