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Noise calculations within the second-order von Neumann approach

We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix of the system resolved with respect to the number of transported charges enables the evaluation of the noise and higher-order cumulants of the full counting statistics. We apply this formalism to an analytically solvable model of a single-level quantum dot coupled to highly biased leads with Lorentzian energy-dependent tunnel coupling and demonstrate that, although reproducing exactly the mean current, the resonant tunneling approximation is not exact for the noise and higher order cumulants. Even if it may fail in the regime of strongly non-Markovian dynamics, this approach generically improves results of lower-order and/or Markovian approaches.