Conductance Fluctuations at the Integer Quantum Hall Plateau Transition

We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a two-terminal conductance $G$ for square samples, considering both periodic and open boundary conditions transverse to the current. At the plateau transition, $G$ is broadly distributed, with a distribution function close to uniform on the interval between zero and one in units of $e^2/h$. Our results are consistent with a recent experiment by Cobden and Kogan on a mesoscopic quantum Hall effect sample.