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Register a new userIrreversible dynamics of vortex reconnections in quantum fluids
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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 a 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 in Proment and Krstulovic (arXiv:2005.02047), 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.
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Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we prove that in thermalised flows $lambda propto sqrt{T}$, in agreement with results from frustrated spin systems. This reveals an underlying universality and provides evidence for recent conjectures on the thermal scaling of $lambda$. We also reconcile seemingly disparate effects -- equilibration on one hand and pushing systems out-of-equilibrium on the other -- of many-body chaos by relating $lambda$ to $T$ through the dynamical structures of the flow.
Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii $R$ in superfluid $^4$He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value $500{rm ,cm}^{-2} R^{-1}$ independent of the injected density. This is due to collisions between rings causing piling-up of many other vortex rings. Both observations are in quantitative agreement with our theory.
We study the evolution of a reactive field advected by a one-dimensional compressible velocity field and subject to an ignition-type nonlinearity. In the limit of small molecular diffusivity the problem can be described by a spatially discretized system, and this allows for an efficient numerical simulation. If the initial field profile is supported in a region of size l < lc one has quenching, i.e., flame extinction, where lc is a characteristic length-scale depending on the system parameters (reacting time, molecular diffusivity and velocity field). We derive an expression for lc in terms of these parameters and relate our results to those obtained by other authors for different flow settings.
This book introduces the theoretical description and properties of quantum fluids. The focus is on gaseous atomic Bose-Einstein condensates and, to a minor extent, superfluid helium, but the underlying concepts are relevant to other forms of quantum fluids such as polariton and photonic condensates. The book is pitched at the level of advanced undergraduates and early postgraduate students, aiming to provide the reader with the knowledge and skills to develop their own research project on quantum fluids. Indeed, the content for this book grew from introductory notes provided to our own research students. It is assumed that the reader has prior knowledge of undergraduate mathematics and/or physics; otherwise, the concepts are introduced from scratch, often with references for directed further reading.
We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $ell$, and a second inertial range for scales smaller than $ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in the decay of quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions using the GPE. We extract the mean free path out of these simulations by measuring the spectral broadening in the Bogoliubov dispersion relation obtained from spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, in order to compare the decay of high temperature quantum and that of classical flows, and to further calibrate the estimations of viscosity from the mean free path in the GPE simulations, we perform low Reynolds number simulations of the Navier-Stokes equations.
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