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

Philipp Strack
Phys. Rev. E 91, 032131 – Published 20 March 2015

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 (KPZ1/f) in spatial dimensions 1d<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<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.

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  • Received 8 August 2014

DOI:https://doi.org/10.1103/PhysRevE.91.032131

©2015 American Physical Society

Authors & Affiliations

Philipp Strack*

  • Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Vol. 91, Iss. 3 — March 2015

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