Dynamic criticality far from equilibrium: One-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance.

Burgers-Kardar-Parisi-Zhang (KPZ) scaling has recently (re-) surfaced in a variety of physical contexts, ranging from anharmonic chains to quantum systems such as open superfluids, in which a variety of random forces may be encountered and/or engineered. Motivated by these developments, we here provide a generalization of the KPZ universality class to situations with long-ranged temporal correlations in the noise, which purposefully break the Galilean invariance that is central to the conventional KPZ solution. We compute the phase diagram and critical exponents of the KPZ equation with 1/f noise (KPZ1/f) in spatial dimensions 1≤d<4 using the dynamic renormalization group with a frequency cutoff technique in a one-loop truncation. Distinct features of KPZ1/f are (i) a generically scale-invariant, rough phase at high noise levels that violates fluctuation-dissipation relations and exhibits hyperthermal statistics even in d=1, (ii) a fine-tuned roughening transition at which the flow fulfills an emergent thermal-like fluctuation-dissipation relation, that separates the rough phase from (iii) a massive phase in 1