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We present a derivation that maps the original problem of a many body openquantum system (OQS) coupled to a harmonic oscillator reservoir into that of amany body OQS coupled to a lattice of harmonic oscillators. The present methodis particularly suitable to analyse the dynamics of atoms arranged in aperiodic structure and coupled the EM field within a photonic crystal. Itallows to solve the dynamics of a many body OQS with methods alternative to thecommonly used master, stochastic Schr\"{o}dinger and Heisenberg equations, andthus to reach regimes well beyond the weak coupling and Born-Markovapproximations.

Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals