Strong acoustic turbulence and the speed of Bose-Einstein condensation

Khlebnikov, Sergei

doi:10.1103/physreva.66.063606

Cited by 7 publications

(7 citation statements)

References 26 publications

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“…18 below suggests an interpretation in terms of acoustic turbulence [37,38,42,46] and corroborates the numerical findings reported in Ref. [73]. The scaling is persistent until late times, see, e.g., Fig.…”

Section: B Acoustic Turbulencesupporting

confidence: 88%

Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas

et al. 2012

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Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analysed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, e.g., in early-universe inflation or quark-gluon plasma dynamics.

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Section: B Acoustic Turbulencesupporting

confidence: 88%

Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas

et al. 2012

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“…The observed scaling corroborates the numerical findings of Ref. [27], whereby we refrain from sharing the interpretation of the power law.…”

supporting

confidence: 90%

Superfluid turbulence: Nonthermal fixed point in an ultracold Bose gas

2011

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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...

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“…The corresponding Porod exponent z = + d 1 also applies to domain walls such as solitons in a ddimensional Bose gas and characterizes the spatial scaling of sound-wave turbulence, see, e.g. [46,86,87]. The rescaled momentum distributions at the non-thermal fixed points studied in the previous section can be fitted, in the infrared momentum region…”

Section: Porod Tailsmentioning

confidence: 95%

“…Another example are magnetic domains in an order-parameter field obeying a O(1) (Z 2 ) symmetric Hamiltonian such as for the Ising model. The corresponding Porod exponent ζ = d + 1 also applies to domain walls such as solitons in a ddimensional Bose gas and characterizes the spatial scaling of sound-wave turbulence, see, e. g. [46,88,89].…”

Section: A Porod Tailsmentioning

confidence: 99%

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

2017

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Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent h - 3 and, related to this, a large dynamical exponent  z 5 are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phaseordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a close connection between the anomalous scaling exponent η, introduced in a quantum-field theoretic approach, and conservation-law induced scaling in classical phase-ordering kinetics is revealed. Moreover, the relation to superfluid turbulence as well as to driven stationary systems is discussed. analysis as well as a comprehensive classification scheme of far-from-equilibrium universal dynamics are lacking so far.Here we consider possible universal scaling behavior of a time-evolving isolated two-dimensional (2D) quantum-degenerate Bose gas quenched far out of equilibrium. We discuss the numerically found scaling in time and in the spatial degrees of freedom in the framework of non-thermal fixed points [34][35][36][37][38]. This approach builds on a scaling analysis of non-perturbative dynamic equations for field correlation functions in the spirit of a renormalization-group approach to far-from-equilibrium dynamics [35,[39][40][41][42][43][44]. Close to a non-thermal fixed point, correlation functions show a time evolution which takes the form of a rescaling in space and time [38]. In consequence, the relaxation is critically slowed down, while correlations evolve as a power law rather than exponentially in time.We prepare far-from-equilibrium states by imprinting phase defects, i.e., quantum vortex excitations, into an otherwise strongly phase-coherent condensate. Different kinds of initial states are realized by varying the number of defects, their arrangement, and their winding numbers. Independently of the microscopic details of the initial state, such as the statistics of fluctuations, the system is attracted to one or more non-thermal fixed points where the information about these details gets lost. Close to such a fixed point the correlations exhibit and evolve according to universal power laws [45][46][47][48][49][50].More than one attractor can exist for the dynamical evolution of the system, as we will demonstrate being the case for the 2D Bose gas studied here. Consequently, different types of universal evolution wit...

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Strong acoustic turbulence and the speed of Bose-Einstein condensation

Cited by 7 publications

References 26 publications

Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas

Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas

Superfluid turbulence: Nonthermal fixed point in an ultracold Bose gas

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

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