  We study the poles of the retarded Green functions of a holographic
superconductor. The model shows a second order phase transition where a charged
scalar operator condenses and a U(1) symmetry is spontaneously broken. The
poles of the holographic Green functions are the quasinormal modes in an AdS
black hole background. We study the spectrum of quasinormal frequencies in the
broken phase, where we establish the appearance of a massless or hydrodynamic
mode at the critical temperature as expected for a second order phase
transition. In the broken phase we find the pole representing second sound. We
compute the speed of second sound and its attenuation length as function of the
temperature. In addition we find a pseudo diffusion mode, whose frequencies are
purely imaginary but with a non-zero gap at zero momentum. This gap goes to
zero at the critical temperature. As a technical side result we explain how to
calculate holographic Green functions and their quasinormal modes for a set of
operators that mix under the RG flow.
