Exact fluctuation relations in voltage- and temperature-biased Laughlin-edge constrictions

Abstract

We present a comprehensive analysis of non-equilibrium fluctuation-dissipation relations connect- ing experimentally accessible chiral-current auto- and cross-correlations to the tunneling-current noise and conductance in Laughlin edge states coupled through a quantum point contact (QPC). We examine their validity for two chiral Laughlin edges held at different temperatures and voltages and show that the relations remain exact for arbitrary tunneling strength, voltage bias, and edge- state temperatures. We further generalize them to spatially extended QPCs and to tunneling am- plitudes with an explicit voltage dependence, and discuss the conditions and limitations associated with these generalizations. Our results establish that the local tunneling-current noise generated at the QPC can be reliably reconstructed from experimentally accessible auto- and cross-correlations measured downstream, providing a robust route to characterize non-equilibrium transport in chiral edge states.