Exponentially small quantum correction to conductance

TL;DR

This paper demonstrates that quantum corrections to conductance in chaotic cavities with broken time-reversal symmetry are exponentially small in the semiclassical limit, derived via a semiclassical approximation unexpectedly capturing an exact correction term.

Contribution

The study reveals an exponentially small quantum correction to conductance due to tunnel barriers, derived semiclassically, and shows this correction is exact despite perturbative assumptions.

Findings

Quantum correction term proportional to b3^M identified

Correction is exponentially small in ar^{-1}

Semiclassical approximation captures an exact correction

Abstract

When time-reversal symmetry is broken, the average conductance through a chaotic cavity, from an entrance lead with $N_1$ open channels to an exit lead with $N_2$ open channels, is given by $N_1N_2/M$, where $M=N_1+N_2$. We show that, when tunnel barriers of reflectivity $\gamma$ are placed on the leads, two correction terms appear in the average conductance, and that one of them is proportional to $\gamma^{M}$. Since $M\sim \hbar^{-1}$, this correction is exponentially small in the semiclassical limit. Surprisingly, we derive this term from a semiclassical approximation, generally expected to give only leading orders in powers of $\hbar$. Even though the theory is built perturbatively both in $\gamma$ and in $1/M$, the final result is exact.