Athermal fluctuations in three dimensional disordered crystals

We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyse the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed perturbation expansion about the crystalline ordered state to three dimensional systems. This allows us to exactly predict changes in positions and forces as a response to the changes in particle radii. We show that fluctuations in forces orthogonal to the lattice directions are highly constrained as compared to the fluctuations along lattice directions. Additionally, we analyse the correlations in the displacement fields produced by the microscopic disorder, which we show displays long ranged behaviour.