Superfluid turbulence: Nonthermal fixed point in an ultracold Bose gas

Abstract

Nonthermal fixed points of far-from-equilibrium dynamics of a dilute degenerate Bose gas are analysed in two and three spatial dimensions. For such systems, universal power-law distributions, previously found within a nonperturbative quantum-field theoretic approach, are shown to be related to vortical dynamics and superfluid turbulence. The results imply an interpretation of the momentum scaling at the nonthermal fixed points in terms of independent vortex excitations of the superfluid. Long-wavelength acoustic excitations on the top of these are found to follow a nonthermal power law. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena studied, e.g., in early-universe inflation or quark-gluon plasma dynamics. , 67.85.DeFrom the formation of Bose-Einstein condensates in ultracold gases to quark-gluon plasmas produced in heavyion collisions, over a range of twentyfour orders of magnitude in temperature, nonequilibrium dynamics governs many interesting phenomena. Turbulence is an outstanding and intricate example, which can be described as an oriented stationary flow of energy or particles between different scales. This idea of an energy cascade goes back to the work of Richardson in the context of atmospheric science [1]. Kolmogorov, in his 1941 mathematical discussion of turbulence in an incompressible fluid, added the concept of universality and scaling [2]. More recently, turbulence has been studied in the context of the inflationary early universe as well as of strongly correlated matter produced in heavy-ion collisions [3][4][5][6][7].Dynamical critical phenomena, i.e., fixed points of the evolution away from thermal equilibrium have been proposed. They potentially affect the equilibration process by forcing the evolution to critically slow down before final thermalization. New scaling laws were found by analysing non-perturbative Kadanoff-Baym dynamic equations [4,5]. Analogous predictions for a nonrelativistic Bose gas were given in [6], proposing strong matterwave turbulence in the regime of long-range excitations.Superfluid turbulence, also referred to as quantum turbulence (QT) has been the subject of extensive studies in the context of helium [9]. In contrast to eddies in classical fluids vorticity in a superfluid is quantized [10,11], and the creation and annihilation processes of quantized vortices are distinctly different [9]. The observation of a Kolmogorov 5/3-law [2] in experiments with superfluid helium, cf.[12] for a review, received much attention [13][14][15][16][17][18][19]. In particular, the role of the normal-fluid as compared to the superfluid component in the turbulent flow * Electronic address: t.gasenzer@uni-heidelberg.de is under debate [9]. In the context of the kinetics of condensation and the development of long-range order in a dilute Bose gas, the role of turbulence in the superfluid and its acoustic excitations was discussed in Refs. [20,21], see also [22] for a recent review. A possible observation...

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

“…In these examples, attractor solutions with self-similar scaling behavior are associated with the phenomenon of Kolmogorov wave turbulence [4,5] and strong turbulence with fluid-like behavior [2,[6][7][8] which leads to Bose condensation far from equilibrium [9][10][11]. A turbulent thermalization mechanism has also been predicted for non-Abelian gauge theories using classical-statistical simulations in a fixed box, where different groups obtain consistent results [12][13][14].…”

“…This is a time-dependent question since for sufficiently late times all classical-statistical descriptions break down once typical occupancies become order one -as is the case for thermal equilibrium 5 -and genuine quantum processes dominate. 6 For weak couplings, the time at which the instability regime ends depends logarithmically on the inverse coupling constant as explained above. The subsequent evolution becomes universal and thus independent of the coupling.…”

“…Since the universal real-time properties at the critical point are controlled by the infrared dynamics, they can be accurately computed within the classical-statistical framework [53]. 6 Here we do not consider the frequently employed possibility to initialize the 'quantum 1/2' only in the instability band [32]. 7 For a vanishing coupling constant (λ = 0) instabilities do not occur and the macroscopic field follows a classical evolution.…”

Numerical Studies of Quantum Turbulence

“…Furthermore, Kobayashi et al generated the stationary steady state QT using the dissipative GP equation and obtained the Kolmogorov law [127,128]. Recently, QT was investigated in terms of a non-thermal fixed point, and the Kolmogorov law was also observed [129,130]. The numerical method for solving the GP equation by pseudo-spectral calculations was well described in Ref.…”

“…Originally, this study focused on superfluid helium, but this result is important for understanding QT in ultracold atomic BECs. After this study, some theoretical works studied QT in ultracold atomic BECs, finding the same Kolmogorov −5/3 law [125,126,127,128,129,130].…”