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

TL;DR

This paper investigates non-thermal fixed points in turbulence models using functional renormalisation group methods, revealing anomalous scaling exponents and connecting classical and quantum turbulence phenomena.

Contribution

It introduces a novel application of functional renormalisation group equations to analyze scaling solutions in Burgers and Gross-Pitaevskii turbulence models, including anomalous exponents.

Findings

Analytical derivation of the Kolmogorov 5/3 exponent for superfluid turbulence.

First results on anomalous exponents in acoustic and quantum turbulence.

Consistency of results with existing experimental data.

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.