Nonequilibrium fluctuation-dissipation relations for one- and two-particle correlation functions in the context of steady-state quantum transport

We study non-equilibrium (NE) fluctuation-dissipation (FD) relations in the context of quantum thermoelectric transport through a two-terminal nanodevice, in the steady-state and with interaction. The FD relations for the one- and two-particle correlation functions are derived. Explicit expressions for the FD relations of the Green's functions (one-particle correlations) are provided. The FD relations for the current-current and charge-charge (two-particle) correlations are calculated numerically. We use self-consistent NE Green's functions calculations to the system in the absence and in the presence of electron-phonon interaction in the central region. We find that the FD relations for the one-particle correlation function are strongly dependent on both the NE conditions and the interactions, while they are much less dependent on the interactions for the two-particle correlation, especially for the current-current correlation functions. This suggests interesting applications for single-molecule and other nanoscale transport experiments. Measurements of the charge and current, and of their fluctuations can provide information about the effective gradients of chemical potential and temperature in the central region, and about other properties of the system such as the strength of the coupling to the leads and of the interaction.