Exponentially small quantum correction to conductance

Lucas H. Oliveira; Pedro H. S. Bento; Marcel Novaes

doi:10.1088/1751-8121/ac93d0

paper

Exponentially small quantum correction to conductance

arXiv:2206.02049 · doi:10.1088/1751-8121/ac93d0

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 $γ$ are placed on the leads, two correction terms appear in the average conductance, and that one of them is proportional to $γ^{M}$ . Since $M \sim ℏ^{- 1}$ , 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 $ℏ$ . Even though the theory is built perturbatively both in $γ$ and in $1/ M$ , the final result is exact.

arXiv comment9 pages, 2 figures

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Cited by in corpus (1)

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