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Multilevel coherences in quantum dots

We study transport through strongly interacting quantum dots with $N$ energy levels that are weakly coupled to generic multi-channel metallic leads. In the regime of coherent sequential tunneling, where level spacing and broadening are of the same order but small compared to temperature, we present a unified, $SU(N)$-invariant form of the kinetic equation for the reduced density matrix of the dot and the tunneling current. This is achieved by introducing the concept of flavor polarization for the dot and the reservoirs, and splitting the kinetic equation in terms of flavor accumulation, anisotropic flavor relaxation, as well as exchange-field- and detuning-induced flavor rotation. In particular, we identify the exchange field as the cause of negative differential conductance at off-resonance bias voltages appearing in generic quantum-dot models. To illustrate the notion of flavor polarization, we analyze the non-linear current through a triple quantum-dot device.