Whispering gallery modes in open quantum billiards

The poles of the S matrix and the wave functions of open two-dimensional quantum billiards with convex boundary of different shape are calculated by using the method of complex scaling. Two leads are attached to the cavities, The conductance of the cavities is calculated at energies with one, two, and three open channels in each lead. Bands of overlapping resonance states appear that are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes known from classical calculations.