  We analyse the dynamical response of a range of 3D Kitaev quantum
spin-liquids, using lattice models chosen to explore the different possible
low-energy spectra for gapless Majorana fermions, with either Fermi surfaces,
nodal lines or Weyl points. We find that the behaviour of the dynamical
structure factor is distinct in all three cases, reflecting the quasiparticle
density of states in two fundamentally different ways. First, the low-energy
response is either straightforwardly related to the power with which the
low-energy density of states vanishes; or for a non-vanishing density of
states, to the phase shifts encountered in the corresponding X-ray edge
problem, whose phenomenology we extend to the case of Majorana fermions.
Second, at higher energies, there is a rich fine-structure, determined by
microscopic features of the Majorana spectrum. Our theoretical results test the
usefulness of inelastic neutron scattering as a probe of these quantum spin
liquids: we find that although spin flips fractionalise, the main features of
the dynamical spin response nevertheless admit straightforward interpretations
in terms of Majorana and flux loop excitations.
