Effect of electromagnetic environment on transport of composite fermions in a narrow constriction between compressible quantum Hall liquids

We elaborate on the recently proposed theory of charge transport through a narrow channel in a compressible quantum Hall liquid. According to Ref. [3], the long-range Coulomb interaction gives rise to the energy-dependent impedance in the effective local Caldeira-Leggett-type action which makes it non-integrable. In this work, we perform an extensive Monte Carlo simulation for the conductance line shape and contrast the numerical results against the predictions made in Ref. [3].