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-levels 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.
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