Abstract
We present a derivation that maps the original problem of a many-body open quantum system (OQS) coupled to a harmonic oscillator reservoir into that of a many-body OQS coupled to a lattice of harmonic oscillators. The present method is particularly suitable to analyze the dynamics of atoms arranged in a periodic structure and coupled with the electromagnetic field within a photonic crystal. It allows to solve the dynamics of a many-body OQS with methods alternative to the commonly used master, stochastic Schr\"odinger, and Heisenberg equations, and thus to reach regimes well beyond the weak coupling and Born-Markov approximations.
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