Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence

Abstract

Scaling in the dynamical properties of complex many-body systems has been of strong interest since turbulence phenomena became the subject of systematic mathematical studies. In this article, dynamical critical phenomena far from equilibrium are investigated with functional renormalisation group equations. The focus is set on scaling solutions of the stochastic driven-dissipative Burgers equation and their relation to solutions known in the literature for Burgers and Kardar-Parisi-Zhang dynamics. We furthermore relate superfluid as well as acoustic turbulence described by the Gross-Pitaevskii model to known analytic and numerical results for scaling solutions. In this way, the canonical Kolmogorov exponent 5/3 for the energy cascade in superfluid turbulence is obtained analytically. We also get first results for anomalous exponents of acoustic and quantum turbulence. These are consistent with existing experimental data. Our results should be relevant for future experiments with, e.g., exciton-polariton condensates in solid-state systems as well as with ultra-cold atomic gases.

22 pages, 4 figures, Published version

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• Prethermalization and universal dynamics in near-integrable quantum systems
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• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• Kinetic theory of non-thermal fixed points in a Bose gas
• Finite temperature spectral functions in the O(N)-model
• Scaling properties of one-dimensional driven-dissipative condensates
• Large-N kinetic theory for highly occupied systems
• Observation of Stable Jones-Roberts Solitons in Bose-Einstein Condensates
• Non-Thermal Fixed Point in a Holographic Superfluid
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• Flowing with the Temporal Renormalisation Group
• Functional Renormalization Group approach to the Kraichnan model
• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• Spectral analysis for compressible quantum fluids
• Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium
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• Superfluid Phase Transition with Activated Velocity Fluctuations: Renormalization Group Approach
• Stability analysis of non-thermal fixed points in longitudinally expanding kinetic theory
• Anomalous scaling at non-thermal fixed points of the sine-Gordon model
• The unpredicted scaling of the one-dimensional Kardar-Parisi-Zhang equation
• Miscible-Immiscible Transition and Nonequilibrium Scaling in Two-Component Driven Open Condensate Wires
• Phase diagram and universal scaling regimes of two-dimensional exciton-polariton Bose-Einstein condensates