We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.

Spectrally truncated three-dimensional (3D) Euler flows reach an absolute equilibrium. Yet they show non-trivial temporal correlations, similar to the ones of turbulent flows. In this work, we investigate Navier-Stokes equation in equilibrium conditions, both at finite viscosity and in the inviscid limit. We determine the space-time velocity correlations, using functional renormalisation group and direct numerical simulations. We characterise the crossover in the dynamical scaling from τ∼ 1/(νk^2) at finite viscosity to τ∼ 1/(u_ rmsk) in the inviscid limit, where τ is the decorrelation time. We show that, although the static properties of spectrally truncated Euler flows radically differ from their hydrodynamical limit, they share a similar emergent k^-1 dynamical scaling.

We develop a theoretical framework that allows us to explore the coupled motion of neutron-superfluid vortices and proton-superconductor flux tubes in a gravitationally collapsed condensate, which describe neutron stars that form pulsars. Our framework uses the 3D Gross-Pitaevskii-Poisson-equation for neutron Cooper pairs, the real-time-Ginzburg-Landau equation for proton Cooper pairs, the Maxwell equations for the vector potential A, and Newtonian gravity and interactions, both direct and induced by the Poisson equation, between the neutron and proton subsystems. For a pulsar we include a crust potential, characterized by an angle theta, and frictional drag. By carrying out extensive direct numerical simulations of this model, we obtain a variety of interesting results. We show that a rotating proton superconductor generates a uniform London magnetic field and the field distribution around flux tubes changes. In the absence of any direct interaction between the two species, they interact through the gravitational Poisson equation. The inclusion of the current-current interaction and the complete Maxwell equations allows us to quantify the entrainment effect that leads to induced magnetization of neutron vortices. We demonstrate that, with a strong external magnetic field B- ext , proton flux tubes are anchored to the crust, whereas neutron vortices leave the condensate and lead to abrupt changes of the crust angular momentum J(c). The frictional term in the dynamical equation for theta yields stick-slip dynamics that leads, in turn, to glitches in the time series of J(c). By calculating various statistical properties of this time series, we demonstrate that they display self-organized criticality that has been found in observations for several pulsars. We compare our results with those of earlier explorations of pulsar-glitch statistics in Gross-Pitaevskii equation-based minimal models for pulsars.

We show how to use the cubic-quintic Gross-Pitaevskii-Poisson equation (cq-GPPE) and the cubic-quintic Stochastic Ginzburg-Landau-Poisson equation (cq-SGLPE) to investigate the gravitational collapse of a tenuous axionic gas into a collapsed axionic condensate for both zero and finite temperature $T$. At $T=0$, we use a Gaussian Ansatz for a spherically symmetric density to obtain parameter regimes in which we might expect to find compact axionic condensates. We then go beyond this Ansatz, by using the cq-SGLPE to investigate the dependence of the axionic condensate on the gravitational strength $G$ at $T = 0$. We demonstrate that, as $G$ increases, the equilibrium configuration goes from a tenuous axionic gas, to flat sheets or $\textit{Zeldovich pancakes}$, cylindrical structures, and finally a spherical axionic condensate. By varying $G$, we show that there are first-order phase transitions, as the system goes from one of these structures to the next one; we find hysteresis loops that are associated with these transitions. We examine these states and the transitions between these states via the Fourier truncated cq-GPPE; and we also obtain the thermalized $T > 0$ states from the cq-SGLPE; the transitions between these states yield thermally driven first-order phase transitions and their associated hysteresis loops. Finally, we discuss how our cq-GPPE approach can be used to follow the spatiotemporal evolution of a rotating axionic condensate and also a rotating binary-axionic-condensate system; in particular, we demonstrate, in the former, the emergence of vortices at large angular speeds $\Omega$ and, in the latter, the rich dynamics of the mergers of the components of this binary system, which can yield vortices in the process of merging.

In this work, we first briefly review some of the mutual friction effects on vortex lines and rings that were obtained in the context of the truncated Gross–Pitaevskii equation in references Krstulovic and Brachet (Phys Rev E 83(6):066311, 2011; Phys Rev B 83:132506, 2011), with particular attention to the anomalous slowdown of rings produced by thermally excited Kelvin waves. We then study the effect of mutual friction on the relaxation and fluctuations of Kelvin waves on straight vortex lines by comparing the results of full 3D direct simulations of the truncated Gross–Pitaevskii equation with a simple stochastic Local-Induction-Approximation model with mutual friction and thermal noise included. This new model allows us to determine the mutual friction coefficient α and α ' for the truncated Gross–Pitaevskii equation.

Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero temperature limit. In quantum flows, like liquid helium II at intermediate temperatures between zero and 2.17 K, a normal fluid and a superfluid coexist with independent velocity fields. The most advanced existing models for such systems use the Navier-Stokes equations for the normal fluid and a simplified description of the superfluid, based on the dynamics of quantized vortex filaments, with ad hoc reconnection rules. There was a single attempt (C. Coste, 1998 [22]) to couple Navier-Stokes and Gross-Pitaevskii equations in a global model intended to describe the compressible two-fluid liquid helium II. We present in this contribution a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid. Coupling terms in the global system of equations involve new definitions of the following concepts: the regularized superfluid vorticity and velocity fields, the friction force exerted by quantized vortices to the normal fluid, the covariant gradient operator in the Gross-Pitaevskii model based on a slip velocity respecting the dynamics of vortex lines in the normal fluid. A numerical algorithm based on pseudo-spectral Fourier methods is presented for solving the coupled system of equations. Finally, we numerically test and validate the new numerical system against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings). The new coupling model has the advantage to keep the full Gross-Pitaevskii model for the superfluid, and thus describe quantized vortex dynamics without any phenomenological approximation. This opens new possibilities to revisit and enrich existing numerical results for complex quantum fluids, such as quantum turbulent flows.

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree. Yet recent numerical simulations in the tensionless (or inviscid) limit of the KPZ equation [Phil. Trans. Roy. Soc. A 380, 20210090 (2022); Phys. Rev. E 106, 024802 (2022)] unveiled a new scaling, with a critical dynamical exponent $z=1$ different from the KPZ one $z=3/2$. In this Letter, we show that this scaling is controlled by a fixed point which had been missed so far and which corresponds to an infinite non-linear coupling. Using the functional renormalization group (FRG), we demonstrate the existence of this fixed point and show that it yields $z=1$. We calculate the correlation function and associated scaling function at this fixed point, providing both a numerical solution of the FRG equations within a reliable approximation, and an exact asymptotic form obtained in the limit of large wavenumbers. Both scaling functions accurately match the one from the numerical simulations.

We consider the Shallow Water equations (SW) on a rotating sphere and their approximation by a finite difference scheme. The discrete unknowns are located at the vertices of the equiangular Cubed Sphere grid, (Croisille, 2013; 2015). The standard fourth order Hermitian difference derivative Lele (1991) is used along a set of suitable great circles. No one sided difference formula is used at any point. All differential operators on the sphere (gradient, divergence and curl) are approximated in a centered fashion. The approximation procedure is close in spirit to the one of compact schemes used in Computational Aeroacoustics. Numerical results on a series of numerical test cases for SW on the sphere are presented. A particular attention is devoted to the temporal scheme. In particular two Rosenbrock exponential time schemes are used and compared to the RK4 scheme. The results demonstrate the interest of the present approach in a variety of situations of interest in numerical climatology.

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces. High resolution (up to $N={2}^{17}$ grid points) numerical simulations of relativistic and nonrelativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm. This paper demonstrates that fluid dynamics can be simulated on NISQs, and opens the door to simulating other fluids, including plasmas, with more general quantum walks and quantum automata.

The one-dimensional Galerkin-truncated Burgers equation, with both dissipation and noise terms included, is studied using spectral methods. When the truncation-scale Reynolds number [Formula: see text] is varied, from very small values to order 1 values, the scale-dependent correlation time [Formula: see text] is shown to follow the expected crossover from the short-distance [Formula: see text] Edwards-Wilkinson scaling to the universal long-distance Kardar-Parisi-Zhang scaling [Formula: see text]. In the inviscid limit, [Formula: see text], we show that the system displays another crossover to the Galerkin-truncated inviscid-Burgers regime that admits thermalized solutions with [Formula: see text]. The scaling forms of the time-correlation functions are shown to follow the known analytical laws and the skewness and excess kurtosis of the interface increments distributions are characterized. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

We develop a minimal self-gravitating model for pulsar glitches by introducing a solid-crust potential in the three-dimensional Gross-Pitaevskii-Poisson equation, which we have used earlier to study gravitationally bound Bose-Einstein condensates, i.e., bosonic stars. In the absence of the crust potential, we show that, if we rotate such a bosonic star, it is threaded by vortices. We then show, via extensive direct numerical simulations, that the interaction of these vortices with the crust potential yields (a) stick-slip dynamics and (b) dynamical glitches. We demonstrate that, if enough momentum is transferred to the crust from the bosonic star, then the vortices are expelled from the star, and the crust's angular momentum J(c) exhibits features that may be interpreted as glitches. From the time series of J(c), we compute the cumulative probability distribution functions (CPDFs) of event sizes, event durations, and waiting times, which are consistent with the previous work. We show that these CPDFs have signatures of self-organized criticality, which are similar to those seen in observations of pulsar glitches and are consistent with previous work.

Since the idea of quantum turbulence was first proposed by Feynman, and later realized in experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been put in finding signatures that distinguish quantum turbulence from its classical counterpart. Here we show that quantum turbulence in rotating condensates is fundamentally different from the classical case. While rotating quantum turbulence develops a negative temperature state with self-organization of the kinetic energy in quantized vortices, it also displays an anisotropic dissipation mechanism and a different, non-Kolmogorovian, scaling of the energy at small scales. This scaling is compatible with Vinen turbulence and is also found in recent simulations of condensates with multicharged vortices. An elementary explanation for the scaling is presented in terms of disorder in the vortices positions.

A new model of nonlinear charged quantum relativistic fluids is presented. This model can be discretized into Discrete Time Quantum Walks (DTQWs), and a new hybrid (quantum-classical) algorithm for implementing these walks on NISQ devices is proposed. High resolution (up to $N=2^{17}$ grid points) hybrid numerical simulations of relativistic and non-relativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm and shown to reproduce equivalent simulations on classical computers. This work demonstrates that nonlinear fluid dynamics can be simulated on NISQs, and opens the door to simulating other, quantum and non-quantum fluids, including plasmas, with more general quantum walks and quantum automata.

We study the long-time decay of rotating turbulence in Bose-Einstein condensates (BECs). We consider the Gross-Pitaevskii equation in a rotating frame of reference and review different formulations for the Hamiltonian of a rotating BEC. We discuss how the energy can be decomposed and present a method to generate out-of-equilibrium initial conditions. We also present a method to generate finite-temperature states of rotating BECs compatible with the Canonical or the Grand canonical ensembles. Finally, we integrate numerically rotating BECs in cigar-shaped traps. A transition is found in the system dynamics as the rotation rate is increased, with a final state of the decay of the turbulent flow compatible with an Abrikosov lattice in a finite-temperature thermalized state.

I first recall the theoretical background relevant to spectral truncation: absolute equilibrium in helical flows and compressible effects. Thermalization phenomenology in Gross-Pitaevskii superflows and thermalization processes in classical systems are then briefly reviewed. The so-called 'tygers' that appear in the truncated inviscid Burgers equation are demonstrated. The basic definitions that relate the Burgers equation to the Kardar-Parisi-Zhang system are recalled. Spectral truncation and conserved quantities are used to introduce the microcanonical and canonical stationary probabilities. The main results on the crossover from absolute equilibrium to Kardar-Parisi-Zhang scaling are finally given after a brief discussion of the relevant physical parameters. The present contribution is thus a short review of the publications, scientific developments and collaborations that went on during the last decade and led to the joint work (Cartes et al., 2022) that I presented at the XVIII Instabilities and Nonequilibrium Structures Workshop held (online) in December 2021 in Valparaiso (Chile), dedicated to the memory of the late Enrique Tirapegui.

We present an alternative form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space (α,β) of the noise, with stability parameter α∈(0,2) and skewness parameter β∈[-1,1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α=2. Three regimes are located at 1<α<2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at 0<α≤1. There, the mean of the noise diverges, and no critical transition occurs. In one case, the origin is always unstable, independently of the distance μ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of μ. We thus demonstrate that an instability subject to nonequilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.