  We generalize the problem of strongly interacting neutron matter by adding a
periodic external modulation. This allows us to study from first principles a
neutron system that is extended and inhomogeneous, with connections to the
physics of both neutron-star crusts and neutron-rich nuclei. We carry out fully
non-perturbative microscopic Quantum Monte Carlo calculations of the energy of
neutron matter at different densities, as well as different strengths and
periodicities of the external potential. In order to remove systematic errors,
we examine finite-size effects and the impact of the wave function ansatz. We
also make contact with energy-density functional theories of nuclei and
disentangle isovector gradient contributions from bulk properties. Finally, we
calculate the static density-density linear response function of neutron matter
and compare it with the response of other physical systems.
