  We study transport through a single-level system placed between two
reservoirs with band-structure, taking strong level-reservoir coupling of the
order of the energy-scales of these band-structures. An exact solution in the
absence of interactions gives the nonlinear Lamb shift. As expected, this moves
the perfectly-transmitting state (the reservoir state that flows through the
single-level without reflection), and can even turn it into a bound-state.
However, here we show that it can also create additional pairs of
perfectly-transmitting states at other energies, when the coupling exceeds
critical values. Then the single-level's transmission function resembles that
of a multi-level system. Even when the discrete level is outside the
reservoirs' bands, additional perfectly-transmitting states can appear inside
the band when the coupling exceeds a critical value. We propose observing the
bosonic version of this in microwave cavities, and the fermionic version in the
conductance of a quantum dot coupled to 1D or 2D reservoirs.
