Abstract
When time-reversal symmetry is broken, the average conductance through a chaotic cavity, from an entrance lead with N₁ open channels to an exit lead with N₂ open channels, is given by N₁N₂/M, where M=N₁+N₂. 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. 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.