Title: Thermalization via three-wave mixing

Abstract: We discuss thermalization in a multimode quantum cavity under unitary evolution. According to general principles, an isolated system with quadratic couplings does not exhibit thermalization. However, we find that three-wave perturbation, typical for instance in superconducting Josephson systems, may lead to thermalization into a Bose-Einstein distribution of occupations of the modes. The temperature of this state is dictated by energy conservation in this closed system, and the thermal distribution is robust against weak disturbances. We discuss how our findings open up new avenues to experimentally probe fundamental assumptions of statistical physics in solid-state systems.