Reservoir-induced phase transitions in bosonic lattice systems

We discuss bosonic lattice systems that are coupled to local reservoirs and driven to non-equilibrium steady states. By engineering the reservoirs we can tailor different phases of steady states that are separated by critical points, where the criticality is defined as a divergence of the correlation length. Free bosonic lattice systems with a linear coupling to reservoirs always show a dynamical instability accompanying the criticality. We investigate interacting many-body systems as well as nonlinear coupling to reservoirs, as, for instance, by saturated gain processes. To this end we employ mean-field approximations as well as numerical methods to derive correlations and critical exponents of the reservoir-induced phase transitions.