Exact Conductance through Point Contacts in theν=1/3Fractional Quantum Hall Effect

Abstract

The conductance for tunneling through an impurity in a Luttinger liquid is described by a universal scaling function. We compute this scaling function exactly, by using the thermodynamic Bethe ansatz and a kinetic (Boltzmann) equation. This model has been proposed to describe resonant tunneling through a point contact between two $\nu =1/3\mathrm{}$ quantum Hall edges. Recent experiments on quantum Hall devices agree well with our exact results. We also derive the exact conductance and $I\left(V\right)$ curve, out of equilibrium, in this fully interacting system.