We establish a new non-equilibrium scaling regime in the short time evolutionof one-dimensional interacting open quantum systems subject to a genericheating mechanism. This dynamical regime is characterized by uncompensatedphonon production and a super-diffusive, universal scaling of quasiparticlelifetimes with momentum $\sim q^{-5/3}$, distinct from finite and zerotemperature cases. It is separated from a high momentum regime by a timedependent scale fading out as $q_0(t) \sim t^{-4/5}$. In the latter region weobserve thermalization to an effective time-dependent equilibrium with linearlyincreasing temperature. By mapping out the dynamical phase diagram andcomputing the dynamical structure factor within an open system Keldyshfunctional integral approach, we show how these predictions can be explored incold atom experiments by means of Bragg spectroscopy.
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