Multi-particle decoherence free subspaces in extended systems

We develop a method to determine spatial configurations to realize decoherence-free subspaces for spatially extended multi-particle systems. We have assumed normal reservoir behavior including translational invariance of the reservoir and preparation in stationary states or mixture thereof and weak Markovian system-reservoir coupling that requires energy transfer. One important outcome of our method is a proof that there does not exist a multi-particle decoherence-free subspace in such systems except in the limit that the spatial extent of the system becomes infinitesimal.