We study electronic transport through metallic multi-island Coulomb-blockade
systems. Based on a diagrammatic real-time approach, we develop a computer
algorithm that generates and calculates all transport contributions up to
second order in the tunnel-coupling strengths for arbitrary multi-island
systems. This comprises sequential and cotunneling, as well as terms
corresponding to a renormalization of charging energies and tunneling
conductances. Multi-island cotunneling processes with energy transfer between
different island are taken into account. To illustrate our approach we analyze
the current through an island in Coulomb blockade, that is electrostatically
coupled to a second island through which a large current is flowing. In this
regime both cotunneling processes involving one island only as well as
multi-island processes are important. The latter can be understood as
photon-assisted sequential tunneling in the blockaded island, where the photons
are provided by potential fluctuations due to sequential tunneling in the
second island. We compare results of our approach to a P(E)-theory for
photon-assisted tunneling in the weak coupling limit.Comment: 14 pages, 7 figures, published version; minor changes in Sec. IV