Wave turbulence in quantum fluids

Abstract

Wave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence. In this short review, we provide a perspective on recent work on WT in quantum fluids, setting it in context and discussing the outlook for the next few years. We outline the theory, review briefly the experiments carried out to date using liquid H 2 and liquid 4 He, and discuss some nonequilibrium excitonic superfluids in which WT has been predicted but not yet observed experimentally. By way of conclusion, we consider the medium-and longer-term outlook for the field.W ave turbulence (WT) (1, 2) is probably less familiar than ordinary (vortex) turbulence to most scientists, but the two sets of phenomena are actually very similar. Unlike electromagnetic waves in the vacuum, which are linear, and can therefore pass through each other unaltered, waves in a nonlinear medium interact with each other, sometimes strongly. WT manifests itself in systems of strongly interacting nonlinear waves. They form a disordered system in which there can be nondissipative flows of energy across the frequency and length scales, much as occur in vortex turbulence. WT arises in a wide variety of classical contexts, including, for example, surface waves on water (both gravity and capillary) (3-5), nonlinear optical systems (6, 7), sound waves in oceanic waveguides (8), shock waves in the solar atmosphere and their coupling to the Earth's magnetosphere (9), and magnetic turbulence in interstellar gases (10). There is a large and rapidly expanding literature, to which many relevant references up to mid-2010 are listed in ref. 2. As we discuss in more detail below, WT can also occur in quantum fluids, where it exhibits some distinctive features. Experimental studies have included surface waves on liquid H 2 (11) and liquid helium (12) and second sound in superfluid 4 He (13). Very recently, WT has been demonstrated and studied numerically in the nonequilibrium excitonic superfluids (14) that occur in semiconductors (15), including graphene (16).In section 1 we review briefly the theory of WT, concentrating on the aspects relevant to quantum fluids. Section 2 describes the relevant experiments reported to date, and also describes a numerical experiment showing that WT can also occur in semiconductor Bose-Einstein condensates (BECs). Finally, in section 4, we conclude and consider the future for research in the area. Theory of Wave Turbulence in...

Introduction to quantum turbulence

“…Their direct observation is reported in the article by Fonda et al (9). At finite temperatures, Kelvin waves are damped by mutual friction, but, below 1 K, they propagate more freely and lead to acoustic emission at large values of k. The transfer of energy to such large k by a Kelvin wave cascade (analogous to the Kolmogorov cascade of classical turbulence) explains the observed decay of turbulence at low temperatures, as discussed in the articles by Barenghi et al (10) and by Walmsley et al (11); in the weak-amplitude regime, Kelvin waves can be studied using wave-turbulence theory [see the article by Kolmakov et al (12)]. …”

Emergence of a turbulent cascade in a quantum gas

“…Our experiments establish the uniform Bose gas as a promising new platform for investigating many aspects of turbulence, including the interplay of vortex and wave turbulence and the relative importance of quantum and classical effects.Compared to classical fluids, superfluids present fascinating peculiarities such as irrotational and frictionless flow, which raises fundamental questions about the character of turbulent cascades [8,9]. Numerous experiments on quantum-fluid turbulence have been performed with liquid helium, exploring both vortex [8,[10][11][12] and wave turbulence [13][14][15], but their theoretical understanding is hampered by the strong interactions that make first-principle descriptions intractable. The situation is a priori simpler for an ultracold weakly interacting Bose gas, which is often accurately described by the GPE for the complex-valued matter field ψ(r, t) [16].…”

Optimal local well-posedness theory for the kinetic wave equation

“…4-wave kinetic equations play an important role in the theory of weak turbulence and appear in several contexts: gravity and capillary waves on the surface of a finite-depth fluid [64,26,27,28,12], Alfven wave turbulence in astrophysical plasmas [46], optical waves of diffraction in nonlinear media [13,40,41], quantum fluids [33], Langmuir waves [62] to name only a few.…”