Breaking of Josephson junction oscillations and onset of quantum turbulence in Bose-Einstein condensates

We analyse the formation and the dynamics of quantum turbulence in a two-dimensional Bose-Einstein condensate with a Josephson junction barrier modeled using the Gross-Pitaevskii equation. We show that a sufficiently high initial superfluid density imbalance leads to randomisation of the dynamics and generation of turbulence, namely, the formation of a quasi-1D dispersive shock consisting of a train of grey solitons that eventually breakup into chains of distinct quantised vortices of alternating vorticity followed by random turbulent flow. The Josephson junction barrier allows us to create two turbulent regimes: acoustic turbulence on one side and vortex turbulence on the other. Throughout the dynamics, a key mechanism for mixing these two regimes is the transmission of vortex dipoles through the barrier: we analyse this scattering process in terms of the barrier parameters, sound emission and vortex annihilation. Finally, we discuss how the vortex turbulence evolves for long times, presenting the optimal configurations for the density imbalance and barrier height in order to create the desired turbulent regimes which last as long as possible

Bose-Einstein condensation and Berezinskii-Kosterlitz-Thouless transition in the two-dimensional nonlinear Schrödinger model

We analyze the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the nonlinear Schrödinger model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first-order correlation function behave with respect to the mass, the energy, and the size of the system. By relating the free-particle energy to the temperature, we are able to estimate the Berezinskii-Kosterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size independent, leading to a power-law dependence of the condensate fraction with respect to the system size

Universal and nonuniversal aspects of vortex reconnections in superfluids

Insight into vortex reconnections in superfluids is presented, making use of analytical results and numerical simulations of the Gross-Pitaevskii model. Universal aspects of the reconnection process are investigated by considering different initial vortex configurations and making use of a recently developed tracking algorithm to reconstruct the vortex filaments. We show that during a reconnection event the vortex lines approach and separate always according to the time scaling $\delta \sim t^{1/2}$ with prefactors that depend on the vortex configuration. We also investigate the behavior of curvature and torsion close to the reconnection point, demonstrating analytically that the curvature can exhibit a self-similar behavior that might be broken by the development of shocklike structures in the torsion

A vortex filament tracking method for the Gross–Pitaevskii model of a superfluid

We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross--Pitaevskii equation. By utilizing the pseudo-vorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems

Starting Flow Past an Airfoil and its Acquired Lift in a Superfluid

We investigate superfluid flow around an airfoil accelerated to a finite velocity from rest. Using simulations of the Gross–Pitaevskii equation we find striking similarities to viscous flows: from production of starting vortices to convergence of airfoil circulation onto a quantized version of the Kutta-Joukowski circulation. We predict the number of quantized vortices nucleated by a given foil via a phenomenological argument. We further find stall-like behavior governed by airfoil speed, not angle of attack, as in classical flows. Finally we analyze the lift and drag acting on the airfoil

Route to thermalization in the α-Fermi–Pasta–Ulam system

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed

Matching theory to characterize sound emission during vortex reconnection in quantum fluids

In a concurrent work, Villois et al. [Phys. Rev. Lett. 125, 164501 (2020)10.1103/PhysRevLett.125.164501] reported the evidence that vortex reconnections in quantum fluids follow an irreversible dynamics, namely, vortices separate faster than they approach; such time asymmetry is explained by using simple conservation arguments. In this work we develop further these theoretical considerations and provide a detailed study of the vortex reconnection process for all the possible geometrical configurations of the order parameter (superfluid) wave function. By matching the theoretical description of incompressible vortex filaments and the linear theory describing locally vortex reconnections, we determine quantitatively the linear momentum and energy exchanges between the incompressible (vortices) and the compressible (density waves) degrees of freedom of the superfluid. We show theoretically and corroborate numerically, why a unidirectional density pulse must be generated after the reconnection process and why only certain reconnecting angles, related to the rates of approach and separations, are allowed. Finally, some aspects concerning the conservation of center-line helicity during the reconnection process are discussed

Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in Helium II is observed. The topology of the tangle is then investigated showing that linked rings may appear during the evolution. The tracking also allows for determining the statistics of small-scales quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade

Irreversible dynamics of vortex reconnections in quantum fluids

We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross-Pitaevskii model. Despite the time reversibility of the model, we report clear evidence that the dynamics of the reconnection process is time irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently by Proment and Krstulovic [Phys. Rev. Fluids 5, 104701 (2020)PLFHBR2469-990X10.1103/PhysRevFluids.5.104701], we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the prospect of being tested in several quantum fluid experiments and, theoretically, may shed new light on the energy transfer mechanisms in both classical and quantum turbulent fluids