  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 analyse the dynamics of atoms arranged in a
periodic structure and coupled the EM 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\"{o}dinger and Heisenberg equations, and
thus to reach regimes well beyond the weak coupling and Born-Markov
approximations.

Quantum Physics