Exact Conductance through Point Contacts in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mspace/><mml:mo>=</mml:mo><mml:mspace/><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn><mml:mn/></mml:math>Fractional Quantum Hall Effect 论文

摘要

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 $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$ 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.