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We study the non-equilibrium dynamics of a disordered quantum systemconsisting of harmonic oscillators in a $d$-dimensional lattice. If the systemis sufficiently localized, we show that, starting from a broad class of initialproduct states that are associated with a tiling (decomposition) of the$d$-dimensional lattice, the dynamical evolution of entanglement follows anarea law in all times. Moreover, the entanglement bound reveals a dependency onhow the subsystems are located within the lattice in dimensions $d\geq 2$. Inparticular, the entanglement grows with the maximum degree of the dual graphassociated with the lattice tiling.

Dynamical Evolution of Entanglement in Disordered Oscillator Systems