Resonant scattering by a loop: the Wigner delay time and Poisson’s kernel

Abstract

The resonances of a loop pierced by a magnetic field are analized in terms of the scattering matrix phase, the Wigner delay time and its relation to Poisson’s kernel. Except for specific values of the magnetic flux, the resonances appear overlapped by pairs due to the broken degeneracy. Although it is well known that the Poisson kernel describes how the phase is distributed in the Argand plane, we demonstrate that Poisson’s kernel coincides with the reciprocal of the Wigner delay time, thus providing a novel interpretation of this quantity. The distribution of the Wigner delay time is also determined, it exhibits explicitly the effect of the magnetic flux, contrary to what happens to the distribution of the phase.