Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect

This paper analyzes the noise of the edge current in a generic fractional quantum Hall state within a tunneling point contact system. The objective is to elucidate the relationship between the non-symmetrized noise in the edge current and the noise in the tunneling current, as well as to establish the effects of the Nyquist-Johnson equilibrium noise. The study provides a comprehensive examination, revealing that the noise from the tunneling current does not simply add to the equilibrium noise; instead, a correction term appears that results from the correlation between the two types of currents. Utilizing a non-equilibrium Ward identity, it is demonstrated that this correction correlates with the anti-symmetric component of the tunneling current noise. Furthermore, findings lead to the formulation of a non-equilibrium fluctuation-dissipation theorem along with relevant expressions for excess and shot noise in the edge current. The methodology employed leverages the principles of charge conservation and chirality, making it applicable to various edge theory constructions involving both non-Abelian states and edges with multiple charged channels. Key tools discussed in this analysis include the non-equilibrium Kubo formula and the non-equilibrium Ward identity.