Theory of a resonant level coupled to several conduction electron channels in equilibrium and out-of-equilibrium
The spinless resonant level model is studied when it is coupled by hopping to one of the arbitrary number of conduction electron channels. The Coulomb interaction acts between the electron on the impurity and in the different channels. In case of repulsive or attractive interaction the conduction electrons are pushed away or attracted to ease or hinder the hopping by creating unoccupied or occupied states, respectively. In the screening of the hopping orthogonality catastrophe plays an important role. In equilibrium the weak and strong coupling limit the renormalizations are treated by perturbative, numerical and Anderson-Yuval Coulomb gas methods. In case of two leads the current due to applied voltage is treated in the weak coupling limit. The presented detailed study should help to test other methods suggested for non-equilibrium transport.