arXiv subjects

Sergey Nazarenko

Publications and source records attributed to Sergey Nazarenko.

At least 37 records · Page 2Linked to original sources

arXiv2023

Direct and inverse cascades in turbulent Bose-Einstein condensate

When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact non-linearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred towards small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs. We analytically derive the Kolmogorov-Zakharov spectra, including the log-correction to the direct cascade scaling and the universal pre-factor constants for both cascades. We test and corroborate our predictions using high-resolution numerical simulations of the forced-dissipated Gross-Pitaevskii model in a periodic box and the corresponding wave-kinetic equation. Theoretical predictions and data are in excellent agreement, without adjustable parameters. Moreover, in order to connect with experiments, we test and validate our theoretical predictions using the Gross-Pitaevskii model with a confining cubic trap. Our results explain previous experimental observations and suggest new settings for future studies.

cond-mat.quant-gas↗

arXiv2023

Hamiltonian derivation of the point vortex model from the two-dimensional nonlinear Schrödinger equation

We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schr{ö}dinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic vortices on the background of a spatially-infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex, for the first time.

physics.flu-dyn↗

arXiv2023

Analysing spatiotemporal instabilities in magneto-optical traps with the tools of turbulence theory

A large cloud of $^{87}$Rb atoms confined in a magneto-optical trap exhibits, in a certain regime of parameters, spatio-temporal instabilities with a dynamics resembling that of a turbulent fluid. We apply the methods of turbulence theory based on structure function analysis to extract scaling exponents which are compared to known turbulent regimes. This analysis also allows us to make a clear distinction between different instability regimes.

physics.atom-ph↗

arXiv2022

Testing wave turbulence theory for Gross-Pitaevskii system

We test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both the wave-action spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of the GPE data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times. Qualitative agreement between the GPE and the WKE persists also for longer times with some quantitative deviations that may be attributed to the combination of breakdown of the theoretical assumptions underlying the WKE as well as numerical issues. Furthermore, we study how the wave statistics evolves toward Gaussianity in a time scale of the order of the kinetic time.The excellent agreement between direct numerical simulations of the GPE and the WKE provides a new and solid ground to the theory of weak wave turbulence.

physics.flu-dyn↗

arXiv2022

Energy spectrum of two-dimensional acoustic turbulence

We report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for the turbulent energy spectrum, $E(k)=C_1 \sqrt{\varepsilon\, a c_{\rm s} }/k$, of acoustic waves in 2D with almost linear dispersion law, $ω_k = c_{\rm s} k[1+(ak)^2]$, $ ak \ll 1$. Here $\varepsilon$ is the energy flux over scales, and $C_1$ is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates (BECs). The corresponding 3D counterpart of turbulent acoustic spectrum was found over half a century ago, however, due to the singularity in 2D, no solution has been obtained until now. We show the spectrum $E(k)$ is realizable in direct numerical simulations of forced-dissipated Gross-Pitaevskii equation in the presence of strong condensate.

cond-mat.other↗

arXiv2021

Inverse cascade anomalies in fourth-order Leith models

We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrodinger model and for the gravitational waves in the Einstein's vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

physics.flu-dyn↗

arXiv2021

Equilibria and condensates in Rossby and drift wave turbulence

We study the thermodynamic equilibrium spectra of the Charney- Hasegawa-Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross-Pitaevskii equations, which are examples for comparison. We explore how the third invariant considerably enriches the variety of equilibrium spectra that the CHM system can access. In particular we characterise the singular limits of these spectra in which condensates occur, i.e. a single Fourier mode (or pair of modes) accumulate(s) a macroscopic fraction of the total invariants. We show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in CHM systems of finite size: highly anisotropic zonal flows, large-scale isotropic vortices, and vortices at small scale. We show how these condensates are associated with combinations of negative thermodynamic potentials (viz. temperature).

physics.flu-dyn↗

arXiv2021

Comment on "Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory''

In a recent paper [T. Tanogami Phys. Rev. E 103, 023106 ] proposes a scenario for quantum turbulence where the energy spectrum at scales smaller than the inter-vortex distance is dominated by a quantum stress cascade, in opposition to Kelvin wave cascade predictions. The purpose of the present comment is to highlight some physical issues in the derivation of the quantum stress cascade, in particular to stress that quantization of circulation has been ignored.

cond-mat.other↗

arXiv2021

Theory of anisotropic superfluid He-4 counterflow turbulence

We develop an analytic theory of strong anisotropy of the energy spectra in the thermally-driven turbulent counterflow of superfluid He-4. The key ingredients of the theory are the three-dimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energy-rate equation, which is fully supported by the numerical solution. The two-dimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiment, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a near-classical non-universal cascade-dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters. This article is a part of the theme issue 'Scaling the turbulence edifice'.

cond-mat.other↗

arXiv2021

Non-equilibrium Bose-Einstein Condensation

We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the forcing at high wave numbers, and study propagation of the turbulent spectrum toward the low wave numbers. Our primary goal is to compare the results for the evolving spectrum with the previous results obtained for the kinetic equation of weak wave turbulence. We demonstrate existence of a regime for which good agreement with the wave turbulence results is found in terms of the main features of the previously discussed self-similar solution. In particular, we find a reasonable agreement with the low-frequency and the high-frequency power-law asymptotics of the evolving solution, including the anomalous power-law exponent $x^* \approx 1.24$ for the three-dimensional waveaction spectrum. We also study the regimes of very weak turbulence, when the evolution is affected by the discreteness of the Fourier space, and the strong turbulence regime when emerging condensate modifies the wave dynamics and leads to formation of strongly nonlinear filamentary vortices.

cond-mat.quant-gas↗

arXiv2021

Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics

We develop the theory of weak wave turbulence in systems described by the Schrödinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the Schrödinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schrödinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. We interpret the inverse cascade as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schrödinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schrödinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.

cond-mat.stat-mech↗

arXiv2020

Suppressing thermalization and constructing weak solutions in truncated inviscid equations of hydrodynamics: Lessons from the Burgers equation

Finite-dimensional, inviscid equations of hydrodynamics, such as the zero-viscosity, one-dimensional Burgers equation or the three-dimensional incompressible Euler equation, obtained through a Fourier-Galerkin projection, thermalise---mediated through structures known as tygers [Ray et al., Phys. Rev. E 84, 016301 (2011)]---with an energy equipartition. Therefore, numerical solutions of inviscid partial differential equations, which typically have to be Galerkin-truncated, show a behaviour at odds with the parent equation. We now propose, by using the one-dimensional Burgers equation as a testing ground, a novel numerical recipe, named tyger purging, to arrest the onset of thermalisation and hence recover the true dissipative solution.

physics.flu-dyn↗

arXiv2020

How trapped particles interact with and sample superfluid vortex excitations

Particles have been used for more than a decade to visualize and study the dynamics of quantum vortices in superfluid helium. In this work we study how the dynamics of a collection of particles set inside a vortex reflects the motion of the vortex. We use a self-consistent model based on the Gross-Pitaevskii equation coupled with classical particle dynamics. We find that each particle oscillates with a natural frequency proportional to the number of vortices attached to it. We then study the dynamics of an array of particles trapped in a quantum vortex and use particle trajectories to measure the frequency spectrum of the vortex excitations. Surprisingly, due to the discreetness of the array, the vortex excitations measured by the particles exhibits bands, gaps and Brillouin zones, analogous to the ones of electrons moving in crystals. We then establish a mathematical analogy where vortex excitations play the role of electrons and particles that of the potential barriers constituting the crystal. We find that the height of the effective potential barriers is proportional to the particle mass and the frequency of the incoming waves. We conclude that large-scale vortex excitations could be in principle directly measured by particles and novel physics could emerge from particle-vortex interaction.

cond-mat.other↗

arXiv2020

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 modelled 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.

cond-mat.quant-gas↗

arXiv2019

The Vortex-Particle Magnus Effect

Experimentalists use particles as tracers in liquid helium. The intrusive effects of particles on the dynamics of vortices remain poorly understood. We implement a study of how basic well understood vortex states, such as a propagating pair of oppositely signed vortices, change in the presence of particles by using a simple model based on the Magnus force. We focus on the 2D case, and compare the analytic and semi-analytic model with simulations of the Gross-Pitaevskii (GP) equation with particles modelled by dynamic external potentials. The results confirm that the Magnus force model is an effective way to approximate vortex-particle motion either with closed-form simplified solutions or with a more accurate numerically solvable ordinary differential equations (ODEs). Furthermore, we increase the complexity of the vortex states and show that the suggested semi-analytical model remains robust in capturing the dynamics observed in the GP simulations.

cond-mat.quant-gas↗

arXiv2019

Phase transition in time-reversible Navier-Stokes equations

We present a comprehensive study of the statistical features of a three-dimensional time-reversible Navier-Stokes (RNS) system, wherein the standard viscosity $ν$ is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the statistical features of the RNS steady states in terms of a non-negative dimensionless control parameter $\mathcal{R}_r$, which quantifies the balance between the fluctuations of kinetic energy at the forcing length scale $\ell_{\rm f}$ and the total energy $E_0$. We find that the system exhibits a transition from a high-enstrophy phase at small $\mathcal{R}_r$, where truncation effects tend to produce partially thermalized states, to a hydrodynamical phase with low enstrophy at large $\mathcal{R}_r$. Using insights from a diffusion model of turbulence (Leith model), we argue that the transition is in fact akin to a continuous phase transition, where $\mathcal{R}_r$ indeed behaves as a thermodynamic control parameter, e.g., a temperature, the enstrophy plays the role of an order parameter, while the symmetry breaking parameter $h$ is (one over) the truncation scale $k_{\rm max}$. We find that the signatures of the phase transition close to the critical point $\mathcal{R}_r^\star$ can essentially be deduced from a heuristic mean-field Landau free energy. This point of view allows us to reinterpret the relevant asymptotics in which the dynamical ensemble equivalence conjectured by Gallavotti, Phys.Lett.A, 223, 1996 could hold true. Our numerics indicate that the low-order statistics of the 3D RNS are indeed qualitatively similar to those observed in direct numerical simulations of the standard Navier-Stokes (NS) equations with viscosity chosen so as to match the average value of the reversible viscosity.

physics.flu-dyn↗

arXiv2019

On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials

We derive a new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form with the 4-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of self-similar solutions for the porous medium equation. These solutions spread infinitely as time goes to infinity and this fact answers the 'weak turbulence' question for the nonlinear Schrödinger equation with random potentials positively. We also derive Ohm's law for the porous medium equation.

math-ph↗

arXiv2019

Rotating magnetohydrodynamic turbulence

Turbulence in rotating Magneto-hydrodynamic systems is studied theoretically and numerically. In the linear limit, when the velocity and magnetic perturbations are small, the system supports two types of waves. When the rotation effects are stronger than the ones of the external magnetic field, one of these waves contains most of the kinetic energy (inertial wave) and the other -- most of the magnetic energy (magnetostrophic wave). The weak wave turbulence (WWT) theory for decoupled inertial and magnetospheric wave systems was previously derived by Galtier (2014). In the present paper, we derive theory of strong turbulence for such waves based on the critical balance (CB) approach conjecturing that the linear and nonlinear timescales are of similar magnitudes in a wide range of turbulent scales. Regimes of weak and strong wave turbulence are simulated numerically. The results appear to be in good agreement with the WWT and CB predictions, particularly for the exponents of the kinetic and magnetic energy spectra.

physics.plasm-ph↗