Exponentially small quantum correction to conductance

Abstract

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 ∼ ℏ −1, this correction is exponentially small in the semiclassical limit. 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.