Quantum stochastic models with hydrodynamical behaviour

We construct a class of quantum stochastic models of reservoir driven many-particle systems that are the natural counterparts of certain extensively studied classical ones, which have been shown to exhibit good hydrodynamical behaviour. Our treatment of these models achieves two main aims. The first is to show that they enjoy the hydrodynamical properties of their classical counterparts. The second is to show that they satisfy the key assumptions of the general quantum macrostatistical scheme, presented in earlier works by the author, which served to expose certain generic large scale features of nonequilibrium steady states, e.g. the long range hydrodynamical correlations that they carry. In this way we establish the viability of that scheme.