Role of Many-particle excitations in Coulomb Blockaded Transport

We discuss the role of electron-electron and electron-phonon correlations in current flow in the Coulomb Blockade regime, focusing specifically on nontrivial signatures arising from the break-down of mean-field theory. By solving transport equations directly in Fock space, we show that electron-electron interactions manifest as gateable excitations experimentally observed in the current-voltage characteristic. While these excitations might merge into an incoherent sum that allows occasional simplifications, a clear separation of excitations into slow `traps' and fast `channels' can lead to further novelties such as negative differential resistance, hysteresis and random telegraph signals. Analogous novelties for electron-phonon correlation include the breakdown of commonly anticipated Stokes-antiStokes intensities, and an anomalous decrease in phonon population upon heating due to reabsorption of emitted phonons.