arXiv subjects

Giorgio Krstulovic

Publications and source records attributed to Giorgio Krstulovic.

At least 19 recordsLinked to original sources

arXiv2026

Universal self-similar evolution of two-dimensional acoustic turbulence in Bose-Einstein condensates

When driven out of equilibrium, a Bose-Einstein condensate develops nonlinearly interacting density waves that trigger a turbulent cascade, transferring energy toward small scales. In this Letter, we investigate the nonstationary evolution of solutions to the two-dimensional Gross-Pitaevskii equation (GPE). Through numerical simulations of both the GPE and the corresponding Wave Kinetic Equation (WKE), we identify self-similar solutions relevant to turbulence in atomic and polariton Bose-Einstein Condensates. These solutions correspond to a new type of non-thermal fixed point and exhibit characteristics of both first and second kind self-similarity. In particular, we show that the dynamics of the propagating front is universal, governed by a dimensionless universal constant $β$, which we determine numerically.

cond-mat.quant-gas↗

arXiv2026

Wave Kinetics and Thermalization in Kadomtsev-Petviashvili-I System

We study properties of solutions, both evolving and equilibrium of the wave-kinetic equation describing ensembles of weak random waves governed by the Kadomstev-Petviashivli-I equations. The latter equation is integrable by the inverse scattering method, and yet it allows resonant wave interactions leading to redistribution of energy in the Fourier space. Such resonant interactions preserve an infinite number of invariants and we find that they preserve compactness of Fourier space supports. Numerically, we observe that the system can thermalize to one of the equilibrium states of Rayleigh-Jeans type, despite the common empirical belief that thermalization is impossible for integrable systems. The thermalized states are formed via non-local spectral transfers leading to creation of strong low-wavenumber peaks of the wave spectrum -- a process akin to Bose-Einstein condensation.

nlin.CD↗

arXiv2026

Cascades in the Kinetic Equation for the Majda-McLaughlin-Tabak model

The Majda-McLaughlin-Tabak (MMT) family of models has proven to be an efficient ground for benchmarking wave turbulence theory, thanks to the low computational cost required to test theoretical ideas and the possibility of tuning nonlinearity and dispersive properties of the equations. Here, we study numerically the wave kinetic equation (WKE) associated with the MMT model and perform simulations to study turbulent cascades. We confirm numerically the predictions of wave turbulence theory, both in the parameter space region where the wave kinetic equation was proven to be well posed and outside of it. We also observe a new stable stationary state in a region where no cascade solutions are expected, a region that, to the best of our knowledge, has not been explored before. Moreover, following recent work, we study next-to-leading-order corrections to the wave kinetic equation; we uncover incurable divergences in the one-dimensional MMT model and, more generally, in higher-dimensional systems with concave power-law dispersion relations.

physics.flu-dyn↗

arXiv2026

Pressure and Size Dependence of Roton Emission and Vortex Creation by Moving Objects in He~II in $T \to 0$ Limit: Generalized Nonlocal Gross-Pitaevskii Model

In the framework of generalized, nonlocal Gross-Pitaevskii (GP) model, we study numerically the pressure- and size-dependent mechanisms of roton emission and vortex nucleation by objects moving in superfluid $^4$He. As far as the authors are aware, this is the first attempt to analyze the pressure dependence of these mechanisms and the associated critical velocities within a single theoretical framework. For each of several pressures in the range from 0 to the solidification pressure of $\approx25$~bar, we chose the parameters of the interatomic interaction potential such that the resulting excitation spectrum for the generalized, nonlocal GP equation approximates fairly accurately the pressure-dependent dispersion curve determined experimentally by Godfrin \textit{et al.}, Phys. Rev. B \textbf{103}, 104516 (2021). In the two-dimensional approximation, for circular obstacles (disks) moving in quiescent $^4$He, we calculated two critical velocities -- one corresponding to the roton emission and the other to the nucleation of quantized vortices -- as functions of pressure and the obstacle's size. We also comment briefly on three-dimensional simulations of the roton emission and vortex nucleation by moving spherical obstacles.

cond-mat.quant-gas↗

arXiv2026

Turbulence and far-from-equilibrium equation of state of Bogoliubov waves in Bose-Einstein Condensates

Bogoliubov waves are fundamental excitations of Bose-Einstein Condensates (BECs). They emerge from a perturbed ground state and interact nonlinearly, triggering turbulent cascades. Here, we study turbulent BECs theoretically and numerically using the 3D Gross-Pitaevskii model and its associated wave-kinetic equations. We derive a new Kolmogorov-like stationary spectrum for short Bogoliubov waves and find a complete analytical expression for the spectrum in the long-wave acoustic regime. We then use our predictions to explain the BEC equation of state reported by Dogra et al. (Nature 620, 521, 2023), and to suggest new experimental settings.

cond-mat.quant-gas↗

arXiv2026

Strong and weak wave turbulence regimes in Bose-Einstein condensates

When a turbulent Bose-Einstein condensate is driven out-of-equilibrium at a scale much smaller than the system size, nonlinear wave interactions transfer particles towards large scales in an inverse cascade process. In this work, we study numerically wave turbulence in a three-dimensional Bose-Einstein condensate in forced and dissipated inverse cascade settings. We observe that when the forcing rate increases, thereby increasing the particle flux, the turbulence spectrum gradually transitions from the weak-wave Kolmogorov-Zakharov cascade to a critical balance state characterized by a range of scales with balanced linear and nonlinear dynamic timescales. Further forcing increases lead to a coherent condensate component superimposed with Bogoliubov-type acoustic turbulence. The role of vortices in such a strongly forced state is marginal, which makes this new state very different from the strongly turbulent state composed of a tangle of quantized vortex lines. We then use our predictions and numerical data to formulate a new out-of-equilibrium equation of state for the 3D inverse cascade.

cond-mat.quant-gas↗

arXiv2026

Quantum vortex driven Kelvin wave in the thermal background of superfluid helium

We present numerical evidence that Kelvin waves (KWs) on quantized vortices in superfluid helium can be directly observed in the normal fluid component at finite temperatures. Using the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) model, we analyze the propagation and temperature dependence of KWs by simultaneously measuring the dispersion of waves on the vortex displacement and the normal fluid velocity. The results demonstrate that the normal fluid supports a coherent KW-like response, with a dispersion relation matching that of the vortex filament (VF). Unlike the Schwarz model where there is almost no temperature dependence, in FOUCAULT KWs frequency and damping both depend on temperature, highlighting the role of mutual friction in mediating the coupling between the two fluids. These findings open a pathway for experimental observation of KWs in the normal phase using tracer based visualization.

physics.flu-dyn↗

arXiv2026

Kelvin wave and soliton propagation in classical viscous vortex filaments

Vortex filaments are highly rotating localized structures of fluids that admits several types of excitation. Here, we study them by using numerical simulations of the three-dimensional incompressible Navier-Stokes equations. We first address the propagation of Kelvin waves, helicoidal excitations propagating along the filament, and measure their dispersion relation which turns out to be in good agreement with the original Lord Kelvin predictions. Then, inspired by the connection between vortex line dynamics and an integrable system, we show numerically the existence of solitons propagating along vortex filaments and study the collision of two of such structures. Finally, we show numerically the experimental feasibility of studying vortex solitons in the lab, by proposing an experiment for their generation.

physics.flu-dyn↗

arXiv2026

Stability of stationary solutions in Acoustic wave turbulence

We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and 3D equilibrium Rayleigh-Jeans and non-equilibrium Kolmogorov-Zakharov solutions. In particular, we show that the stability of these solutions is ensured by different mechanisms.

nlin.CD↗

arXiv2025

Inverse energy transfer in three-dimensional quantum vortex flows

Vortex reconnections play a fundamental role in fluids.They increase the complexity of flow and develop small-scale motions.In this work, we report that in superfluids, they can also excite large scales. We numerically illustrate that during a superfluid vortex reconnection energy is injected into the thermal (normal) component of helium~II at small length scales, but is transferred nonlinearly to larger length scales, increasing the integral length scale of the normal fluid. We show, by studying about fifty different reconnections, that this inverse energy transfer is triggered by the helical imbalance generated in the normal fluid flow by the mutual friction force coupling the superfluid vortices and the normal component. We finally discuss the relevance of our findings to the problem of superfluid turbulence.

physics.flu-dyn↗

arXiv2025

Quantum vortices leave a macroscopic signature in the normal fluid

Recent work has highlighted the remarkable properties of quantum turbulence in superfluid helium II, consisting of a disordered tangle of quantised vortex lines which interact with each other and reconnect when they collide. According to Landau's two-fluid theory, these vortex lines move in a surrounding of thermal excitations called the normal fluid. Until now, the normal fluid has often been considered a passive background which simply provides the vortex lines with a mechanism for dissipating their kinetic energy into heat. Using a model which fully takes into account the two-way interaction between the vortex lines and the normal fluid, here we show numerically that each vortex line creates a macroscopic wake in the normal fluid that can be larger than the average distance between vortex lines; this is surprising, given the microscopic size of the superfluid vortex cores which induce these wakes. We show that in heat transfer experiments, the flow of the normal fluid can therefore be described as the superposition of an imposed uniform flow and wakes generated by the vortex lines, leading to non-classical statistics of the normal fluid velocity. We also argue that this first evidence of independent fluid structures in the thermal excitations postulated by Landau may be at the root of recent, unaccounted for, experimental findings.

physics.flu-dyn↗

arXiv2025

Experimental and theoretical evidence of universality in superfluid vortex reconnections

The minimum separation between reconnecting vortices in fluids and superfluids obeys a universal scaling law with respect to time. The pre-reconnection and the post-reconnection prefactors of this scaling law are different, a property related to irreversibility and to energy transfer and dissipation mechanisms. In the present work, we determine the temperature dependence of these prefactors in superfluid helium from experiments and a numeric model which fully accounts for the coupled dynamics of the superfluid vortex lines and the thermal normal fluid component. At all temperatures, we observe a pre- and post-reconnection asymmetry similar to that observed in other superfluids and in classical viscous fluids, indicating that vortex reconnections display a universal behaviour independent of the small-scale regularising dynamics. We also numerically show that each vortex reconnection event represents a sudden injection of energy in the normal fluid. Finally we argue that in a turbulent flow, these punctuated energy injections can sustain the normal fluid in a perturbed state, provided that the density of superfluid vortices is large enough.

cond-mat.quant-gas↗

arXiv2025

WavKinS.jl : an efficient and modular Julia software for solving wave kinetic equations

This article describes the Wave Kinetic Solver \WavKinSns, a software developed in the Julia language for solving different types of wave kinetic equations in an efficient and modular manner. \WavKinS already solves the wave kinetic equation describing the interaction of waves in several physical systems, such as acoustic waves, Bose-Einstein condensates, internal gravity waves and many others. Thanks to the structures and routines already implemented in \WavKinSns, we expect that developing a new solver for a specific physical system to be straightforward. \WavKinS is an Open Source project distributed with EUPL-1.2 license agreement.

nlin.CD↗

arXiv2025

Wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves

Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. During the early evolution, three well-known nonlocal interactions, the Elastic Scattering, the Induced-Diffusion, and the Parametric Subharmonic Instability, together with a Superharmonic Resonance play a prominent role. In contrast, local interactions are responsible for anisotropic energy cascade on longer time scales. We reveal emergence of a condensate at small horizontal wavevectors that can be interpreted as a pure wave-wave interaction-mediated layering process.

physics.flu-dyn↗

arXiv2025

Capture and release of quantum vortices using mechanical devices in low-temperature superfluids

We show that the Gross-Pitaevskii equation coupled with the wave equation for a wire (GP-W) provides a natural theoretical framework for understanding recent experiments employing a nanowire to detect a single quantum vortex in superfluid $^4 {\rm He}$. We uncover the complete spatiotemporal evolution of such wire-based vortex detection via direct numerical simulations of the GP-W system. Furthermore, by computing the spatiotemporal spectrum, we obtain the vortex-capture-induced change in the oscillation frequency of the wire. We quantify this frequency shift by plotting the wire's oscillation frequency versus time and obtain results that closely match experimental observations. In addition, we provide analytical support for our numerical results by deriving the dispersion relation for the oscillating wire, with and without a trapped vortex. We show that the Magnus force opens a gap in the wire dispersion relation. The size of the gap becomes the characteristic frequency of the wire when a vortex is trapped.

cond-mat.other↗

arXiv2024

Lack of self-similarity in transverse velocity increments and circulation statistics in two-dimensional turbulence

We study the statistics of longitudinal and transverse structure functions, as well as velocity circulation in the inverse energy cascade of two-dimensional turbulence. By means of direct numerical simulations of the incompressible Navier-Stokes equations, we show that transverse structure functions exhibit an anomalous scaling, in contrast to the self-similar behavior of longitudinal ones. We derive an analytical relation that shows that the scaling exponents of transverse structure functions and velocity circulation are related in two-dimensional turbulence.

physics.flu-dyn↗

arXiv2024

An upper critical dimension for dynamo action: A $d$-dimensional closure model study

We construct a $d$-dimensional Eddy Damped Quasi-Normal Markovian (EDQNM) Closure Model to study dynamo action in arbitrary dimensions. In particular, we find lower $d_L$ and upper $d_U$ critical dimensions for sustained dynamo action in this incompressible problem. Our model is adaptable for future studies incorporating helicity, compressible effects and a wide range of magnetic Reynolds and Prandtl numbers.

physics.plasm-ph↗

arXiv2024

On the kinetics of internal gravity waves beyond the hydrostatic regime

We present a new derivation of the kinetic equation for weak, non-hydrostatic internal gravity wave turbulence. The equation is equivalent to the one obtained by Caillol & Zeitlin (2000), but it takes a canonical form. We show that it conserves the energy without involving the resonance condition in frequency, and look for the isotropic part of the steady, scale invariant solutions. We provide a parametrization of the resonant manifold of non-hydrostatic internal gravity wave triadic interactions. This allows us to simplify the collision integral, and to evaluate the transfer coefficients of all triadic interactions. In the hydrostatic limit, our equation is equivalent to the Hamiltonian description of Lvov & Tabak (2001).

physics.flu-dyn↗