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We study the interplay of disorder with pumping and decay in coupledqubit-cavity arrays, the Jaynes-Cummings-Hubbard model. We find that relativelyweak disorder can wash out the bistability present in the clean pumped system,and that moreover, the combination of disorder in on-site energies and decaycan lead to effective phase disorder. To explore these questions, we present anon- equilibrium generalisation of Stochastic-Mean-Field theory, providing asimple tool to address such questions. This technique is developed for rathergeneral forms of light-matter coupling, driving, dissipation, and on-sitedisorder, making it applicable to a wide range of systems.

Disordered driven coupled cavity arrays: Non-equilibrium stochastic mean-field theory