  A condensate of pairs in an isolated, homogeneous, unpolarised, finite-size
spin 1/2 Fermi gas at low nonzero temperature T, undergoes with time a phase
change with a random component, due to coupling to the gas thermal phonons.
With the quantum second Josephson relation relating the derivative of the
condensate phase operator to the phonon occupation numbers, and linearised
kinetic equations giving the evolution of occupation number fluctuations, we
access the behaviour of the phase change variance at times much longer than the
phonon collision time. The case of a convex phonon branch is similar to the
Bose gas case: the leading collisional processes are the Beliaev-Landau
3-phonons processes, and the variance is the sum of a ballistic term and of a
delayed diffusive term, whose analytical expressions are given in the
thermodynamic limit. The concave case is more exotic. It is analysed at time
scales $T^{-9}$, allowing one to restrict to 2 phonons $\rightarrow$ 2 phonons
small-angle Landau-Khalatnikov processes. The total number of phonons is
conserved and the phonon mean occupation numbers at equilibrium can exhibit a
negative chemical potential, assumed isotropic. The phase change variance is
then the sum of a ballistic term, of a diffusive term, of exotic subsubleading
terms and of a constant term. The analytic expression of some of the
corresponding coefficients is obtained, as well as the diverging leading
behavior of the other ones when the phonon chemical potential tends to 0. When
this chemical potential is 0, the variance sub-ballistic part becomes
superdiffusive, with an exponent 5/3 and an exactly-known coefficient. For a
nonzero infinitesimal phonon chemical potential, a law is found, interpolating
between superdiffusive and diffusive phase spreading. Also new results are
obtained on the phonon Landau-Khalatnikov damping rate, in particular at
negative phonon chemical potential.
