Recent experimental progress has made it possible to detect in real-time
single electrons tunneling through Coulomb blockade nanostructures, thereby
allowing for precise measurements of the statistical distribution of the number
of transferred charges, the so-called full counting statistics. These
experimental advances call for a solid theoretical platform for equally
accurate calculations of distribution functions and their cumulants. Here we
develop a general framework for calculating zero-frequency current cumulants of
arbitrary orders for transport through nanostructures with strong Coulomb
interactions. Our recursive method can treat systems with many states as well
as non-Markovian dynamics. We illustrate our approach with three examples of
current experimental relevance: bunching transport through a two-level quantum
dot, transport through a nano-electromechanical system with dynamical
Franck-Condon blockade, and transport through coherently coupled quantum dots
embedded in a dissipative environment. We discuss properties of high-order
cumulants as well as possible subtleties associated with non-Markovian
dynamics.Comment: 27 pages, 8 figures, 1 table, final version as published in Phys.
Rev.
