| Summary: | We consider an integrable system of two one-dimensional fermionic chains
connected by a link. The hopping constant at the link can be different from
that in the bulk. Starting from an initial state in which the left chain is
populated while the right is empty, we present time-dependent full counting
statistics and the Loschmidt echo in terms of Fredholm determinants. Using this
exact representation, we compute the above quantities as well as the current
through the link, the shot noise and the entanglement entropy in the large time
limit. We find that the physics is strongly affected by the value of the
hopping constant at the link. If it is smaller than the hopping constant in the
bulk, then a local steady state is established at the link, while in the
opposite case all physical quantities studied experience persistent
oscillations. In the latter case the frequency of the oscillations is
determined by the energy of the bound state and, for the Loschmidt echo, by the
bias of chemical potentials.
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