Title: Stabilization of prethermal Floquet steady states in a periodically driven dissipative Bose-Hubbard model,
Abstract: We discuss the effect of dissipation on heating which occurs in periodically
driven quantum many body systems. We especially focus on a periodically driven
Bose-Hubbard model coupled to an energy and particle reservoir. Without
dissipation, this model is known to undergo parametric instabilities which can
be considered as an initial stage of heating. By taking the weak on-site
interaction limit as well as the weak system-reservoir coupling limit, we find
that parametric instabilities are suppressed if the dissipation is stronger
than the on-site interaction strength and stable steady states appear. Our
results demonstrate that periodically-driven systems can emit energy, which is
absorbed from external drivings, to the reservoir so that they can avoid
heating.