Abstract
We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a [Formula: see text]-dimensional lattice. If the system is sufficiently localized, we show that, starting from a broad class of initial product states that are associated with a tiling (decomposition) of the [Formula: see text]-dimensional lattice, the dynamical evolution of entanglement follows an area law in all times. Moreover, the entanglement bound reveals a dependency on how the subsystems are located within the lattice in dimensions [Formula: see text]. In particular, the entanglement grows with the maximum degree of the dual graph associated with the lattice tiling.
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