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

TL;DR

This paper extends the KPZ universality class to include long-range temporal noise correlations that break Galilean invariance, revealing new phases and critical behavior in non-equilibrium systems.

Contribution

It introduces a generalized KPZ model with 1/f noise, computes its phase diagram and critical exponents, and uncovers novel scale-invariant phases and transitions in dimensions 1 to 4.

Findings

Existence of a scale-invariant rough phase with hyperthermal statistics in 1D.

Identification of a roughening transition with emergent thermal-like fluctuation-dissipation.

Discovery of a massive phase in dimensions greater than one.

Abstract

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 (KPZ$_{1/f}$) in spatial dimensions $1\leq d < 4$ using the dynamic renormalization group with a frequency cutoff technique in a one-loop truncation. Distinct features of KPZ$_{1/f}$ are: (i) a generically scale-invariant, rough phase at high noise levels that violates fluctuation-dissipation relations and exhibits hyperthermal statistics {\it 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 {\it massive phase} in $1< d < 4$ (in $d=1$ the interface is always rough). We point out potential connections to nonlinear hydrodynamics with a reduced set of conservation laws and noisy quantum liquids.