Exponentially small quantum correction to conductance

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 $N_1{N}_2/M$, 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 $M\sim {\hslash }^{-1}$, 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 $\hslash$. Even though the theory is built perturbatively both in $\gamma$ and in $1/M$, the final result is exact.

9 pages, 2 figures

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Cited by in corpus (1)

• Semiclassical roots of universality in many-body quantum chaos