Collective excitations in superconductors belowTc

Fluctuations of tunneling currents through Josephson junctions are investigated for clean superconductors in the vicinity below $T_c$. The collective quasiparticle excitations, leading to a maximum in the structure function of the order-parameter phase, also affect the longitudinal dielectric function $\epsilon$. A minimum in $\mathrm{Im}\left(\frac{1}{\epsilon }\right)$ is the counterpart to the phase maximum. It is also present in dirty samples, but disappears in the gapless case. The longitudinal ultrasonic spectrum is discussed for clean and dirty probes. Besides the ordinary sound one finds a second maximum in the spectrum on account of the collective motion of the electrons below $T_c$.