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Nonequilibrium Fluctuation-Dissipation Theorems for Interacting 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. Numerical applications, using self-consistent NE Green's functions calculations, are given for 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. This suggests interesting applications for single-molecule and other nanoscale transport experiments: the two-particle correlation functions, obtained from noise and transport measurement, provide information about the gradients of chemical potential and temperature, and other properties of the system.