Geodynamics and artificial gravity in space-time crystals under slow perturbation and deformation

Abstract: We present a theory of geodynamics in a space-time crystal based on an event wave packet constructed from the Floquet-Bloch waves, which not only involve a scalar dispersion function but also a Berry curvature tensor in the phase space manifold of space-time and the reciprocal quasi energy-momentum. In the presence of structural deformation, this theory is naturally extended into a covariant form with the introduction of a lattice connection constructed out of the gradients of the local lattice vectors. The geodesic equation for a particle not only involves the lattice connection but also higher-order corrections from space-time inhomogeneity of Berry curvatures and quasi energy-momentum dispersion gradients. These emergent connections and metric terms in the geodesic equations indicate the potential to experimentally realize artificial gravitational effects, thereby establishing a direct conceptual link between general relativity and quantum theory.