Finite frequency noise in a chiral Luttinger liquid coupled to phonons

We study transport between quantum Hall edge states at filling factor ν=1 in the presence of electron-acoustic-phonon coupling. After a Bogoliubov-Valatin transformation, the low-energy spectrum of interacting electron-phonon system is presented. The electron-phonon interaction splits the spectrum into charged and neutral "downstream" and neutral "upstream" modes with different velocities. In the regimes of dc and periodic ac biases the tunneling current and nonequilibrium finite frequency nonsymmetrized noise are calculated perturbatively in tunneling coupling of the quantum point contact. We show that the presence of electron-phonon interaction strongly modifies noise and current relations compared to the free-fermion case.