  Mesoscopic low frequency noise in electrical characteristics of disordered
conductors is a result of dynamic quantum interference pattern due to motion of
defects. This has been firmly established by demonstrating the characteristic
partial suppression of the noise amplitude by the dephasing effect of a weak
external magnetic field. The spatial correlation of the quantum interference
pattern in disordered normal state conductors is invariably limited by the
exponential phase relaxation due to inelastic processes. In this paper we
develop a quantitative theory of the mesoscopic noise in the s-wave
superconducting phase of a strongly disordered superconductor (such that the
superconducting coherence length is much longer than the mean free path). We
find that the superconducting coherence length limits the quantum interference
effects in superconductors. However, in contrast to the normal phase, the decay
of the phase relaxation on the scale of the superconducting coherence length is
non-exponential. This unusual slow relaxation manifests in the enhanced
amplitude of the mesoscopic noise in superconductors and a peculiar non-linear
scaling of the amplitude with the strength/number of mobile defects in very
thin superconducting films and wires (effectively 2D and 1D with respect to the
superconducting coherence length). Mesoscopic noise sets a natural limit on the
quality of kinetic inductance elements.
