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arXiv:2603.18880 · Physical review. D/Physical review. D.

Vortex retention mediated turbulent transitions in self-gravitating bosonic and axionic condensates

Anirudh Sivakumar, Sanjay Shukla, Rahul Anil Pandit, Pankaj Kumar Mishra, Paulsamy Muruganandam

Published May 18, 2026• 0 citations
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Abstract

We investigate turbulent spin-down dynamics in self-gravitating Bose-Einstein condensates, comparing purely bosonic and axionic (higher-order interacting) systems. Through simulations of the Gross-Pitaevskii-Poisson system, we study condensates pinned to a crust potential undergoing rapid rotation slowdown. We find that axionic condensates exhibit more uniform density profiles and smaller sizes compared to their bosonic counterparts for similar interaction strengths, which facilitates earlier vortex entry. The sudden spin-down triggers vortex depinning and a turbulent cascade. For comparable sizes, both systems exhibit a short-lived Kolmogorov energy cascade ($k^{-5/3}$ scaling) followed by a transition to Vinen turbulence ($k^{-1}$ scaling). Crucially, their responses diverge with increasing interaction strength (and thus condensate size): the axionic system increasingly deviates from Kolmogorov scaling because of enhanced vortex retention, a trend quantitatively confirmed by analyzing the vortex fraction and its dependence on the final rotation frequency. Spectral analysis reveals that the growth of incompressible energy is primarily driven by quantum pressure during vortex detachment, rather than by compressible flows. The compressible spectrum shows thermalization ($k$ scaling). Our results demonstrate how distinct nonlinearities govern vortex dynamics and turbulent dissipation in self-gravitating quantum fluids.

DOI
10.1103/2bty-918t

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We investigate turbulent spin-down dynamics in self-gravitating Bose-Einstein condensates, comparing purely bosonic and axionic (higher-order interacting) systems. Through simulations of the Gross-Pitaevskii-Poisson system, we study condensates pinned to a crust potential undergoing rapid rotation slowdown. We find that axionic condensates exhibit more uniform density profiles and smaller sizes compared to their bosonic counterparts for similar interaction strengths, which facilitates earlier vortex entry. The sudden spin-down triggers vortex depinning and a turbulent cascade. For comparable sizes, both systems exhibit a short-lived Kolmogorov energy cascade (k−5/3k^{-5/3}k−5/3 scaling) followed by a transition to Vinen turbulence (k−1k^{-1}k−1 scaling). Crucially, their responses diverge with increasing interaction strength (and thus condensate size): the axionic system increasingly deviates from Kolmogorov scaling because of enhanced vortex retention, a trend quantitatively confirmed by analyzing the vortex fraction and its dependence on the final rotation frequency. Spectral analysis reveals that the growth of incompressible energy is primarily driven by quantum pressure during vortex detachment, rather than by compressible flows. The compressible spectrum shows thermalization (kkk scaling). Our results demonstrate how distinct nonlinearities govern vortex dynamics and turbulent dissipation in self-gravitating quantum fluids.
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Quantum turbulence indicators in dipolar Bose-Einstein condensed fluids, following emissions of vortex-antivortex pairs generated by a circularly moving detuned laser, are being provided by numerical simulations of the corresponding quasi-two-dimensional Gross-Pitaevskii formalism with repulsive contact interactions combined with tunable dipole-dipole strength. The critical velocities of two variants of a circularly moving obstacle are determined and analyzed for vortex-antivortex nucleation in the form of regular and cluster emissions. The turbulent dynamical behavior is predicted to follow closely the initial emission of vortex-antivortex pairs, relying on the expected Kolmogorov classical scaling law, which is verified by the spectral analysis of the incompressible part of the kinetic energy. Within our aim to provide further support in the investigations to date of quantum turbulence, which have been focused on nondipolar Bose-Einstein condensates, we emphasize the role of dipole-dipole interactions in the fluid dynamics.
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We investigate the dynamics of turbulent flow in a two-dimensional trapped Bose-Einstein condensate by solving the Gross-Pitaevskii equation numerically. The development of the quantum turbulence is activated by the disruption of an initially embedded vortex quadrupole. By calculating the incompressible kinetic-energy spectrum of the superflow, we conclude that this quantum turbulent state is characterized by the Kolmogorov-Saffman scaling law in the wave-number space. Our study predicts the coexistence of two subinertial ranges responsible for the energy cascade and enstrophy cascade in this prototype of two-dimensional quantum turbulence.
Identified as a unique regime of fluid flow some 500 years ago, turbulence has fascinated and confounded for centuries. Indeed, a fundamental understanding of the turbulence phenomenon remains one of the most important unsolved problems in classical physics. Interestingly, superfluid atomic Bose-Einstein condensates (BECs) can also be agitated into highly excited states of chaotic vortex motion, suggestive of turbulence. However, in contrast to classical fluids, the vortices in these quantum systems exhibit topological stability, the restriction of quantized circulation, and a well defined length scale characterized by the so-called healing length of the superfluid. Such simplifying aspects motivate the study of turbulence in these systems, which may shed new light on the longstanding classical problem. \n\nWhilst a considerable number of studies have been conducted on turbulence in three-dimensional BEC systems, and such studies have uncovered similarities between the classical and quantum counterparts, including the presence of the Kolmogorov k−5/3k^{-5/3}k−5/3 law in the kinetic energy spectrum and the associated direct energy cascade, comparatively few studies have been conducted on two-dimensional quantum turbulence. An important question for such systems is whether the inverse energy cascade, a defining feature of classical two-dimensional turbulent fluid flows, may occur in these systems. In addition to a Kolmogorov kinetic energy spectrum, this process is signified by the clustering of same-circulation vortices, which results in the emergence of macroscopic vortex structures from the turbulent flow. \n\nAlthough intermittent few-vortex clustering has been observed in the break-down of superfluid flow around an obstacle, current attempts to observe a sustained inverse cascade have been unsuccessful, largely due to complications which arise due to the compressibility of the dilute Bose gas - a feature not considered in the classical theory.\n\nWe present a study of two-dimensional quantum turbulence in atomic BECs within the framework of damped Gross-Pitaevskii theory. With the motivation of determining the existence of the inverse cascade phenomenon in such systems, we focusing on experimentally realistic forcing procedures, and study the details of kinetic energy spectra, the statistics of vortex clustering, and the transport of kinetic energy through scale space in the resulting turbulent flows.\nWe investigate a range of vortex injection regimes produced through the circular stirring of a harmonically confined system with a repulsive Gaussian obstacle potential, identifying distinct regimes of turbulence. In the incompressible regime relevant to the inverse cascade, we identify numerous problems with the system and forcing procedure. Motivated by these findings, we investigate turbulence in a minimal model of the spindown of a toroidal persistent current. In this system, we identify a regime of forcing and damping in which the inverse cascade is corroborated by three independent measures: I) merging of vortex clusters; II) a Kolmogorov scaling in the incompressible kinetic energy spectrum; and III) Spectral condensation, associated with the emergence of large scale rotating structures from the turbulent flow. We provide clear evidence that the inverse cascade phenomenon, previously observed in a range of classical fluid systems, can also occur in quantum turbulence.
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