Scattering echoes in a waveguide with a ripple cavity

We observe time-periodic echoes in the transmitted electron probability for a quantum waveguide with a ripple cavity. Knowing the period of the echoes, we can determine the horseshoe development parameter which characterizes the classical chaotic scattering inside the cavity. We use Husimi plots to identify scattering resonances in the conductance fluctuations supported by the stable and unstable manifolds of the outer fixed points of the ripple cavity. We also investigate the time evolution of a Gaussian wavepacket incident on the ripple cavity and show that the transmitted wavepacket is emitted in periodic pulses. The period of the pulses is consistent with theoretical predictions obtained from the classical phase space and the result which we obtain from the quantum conductance fluctuations.