{"id":"9afbf8ee-24c8-4ec0-8cb9-4939f558a3ac","arxiv_id":"2506.16358","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Rotating quantum turbulence splits into three regimes, with incompressible energy spectra scaling as k^-1, k^-5/3, or k^-2 depending on rotation rate and interactions.","lead":"This paper maps how spinning a quantum fluid changes its turbulence, revealing three distinct regimes with different energy spectra. It combines a review of past experiments and simulations with new supercomputer runs of the Gross-Pitaevskii equation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The regime map is supported mainly by broad, visually selected spectral slopes with no uncertainties, and the sole k^-5/3 point is not clearly in the LLL regime.","rationale":"The paper works as a qualitative roadmap: the review is useful, the simulations show systematic changes with rotation, trap shape, and density, and the use of the publicly available GHOST code plus earlier peer-reviewed work by the same group gives some independent support for the numerical infrastructure. The load-bearing quantitative step is the assignment of distinct spectral exponents to the three regimes. That step is weak in two connected ways. First, the exponents are read from broad histograms with visually chosen windows and no error bars, so the separation between -1, -5/3, and -2 is not established at a stated confidence. Second, the only run assigned the -5/3 exponent, the H-trap run at Omega/omega_perp = 0.95, has reported parameters I = 2.39 and kint*xi ~ 0.8, which imply ell_int ~ 8 xi; this contradicts the text's claim that ell_int approaches xi in this regime and does not satisfy the LLL criterion I << 1 stated in Sec. 2(d)(iii). These issues do not falsify the qualitative picture, but they do mean the central 'three regimes with distinct spectra' claim is not yet tightly constrained. The reader's conditional verdict is therefore appropriate: the paper should be accepted only if the spectral analysis is made objective and uncertainty-quantified, and if the LLL classification of the key -5/3 run is either corrected with direct diagnostics or supported by additional runs.","tokens_in":28237,"tokens_out":16279,"duration_ms":160691,"concrete_test":"Release the time-resolved spectra for all 12 runs and replace the visual selection of Sec. 3(c) with an automated procedure: compute alpha(k,t) from Eq. (3.4), fit a constant alpha over every contiguous k-window of width at least one octave within [k_r, 5 k_int], and repeat for time windows of 0.5, 1, and 1.5 breathing periods after the kint peak (Fig. 2). Bootstrap over the sampled times to obtain a 95% interval for the fitted alpha in each run. If the intervals for runs assigned to -1, -5/3, and -2 overlap by more than 0.3, the three-regime classification is not established. Independently recompute I and ell_int for the Omega/omega_perp = 0.95 H run from the actual central density and vortex positions; if I ~ 2.39 and ell_int ~ 8 xi, that run does not satisfy the paper's own LLL criteria.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that rotating quantum turbulence splits into three regimes with distinct spectral exponents. What carries that claim is the assignment of an exponent alpha to each of the 12 simulations in Fig. 7. But alpha is obtained by visually selecting wave-number ranges and histogramming the logarithmic derivative over a broad range of k and over a time window chosen by hand after the kint peak (Sec. 3(c), Fig. 2). The insets of Figs. 4-6 show histograms whose counts spread over more than one unit of alpha, so the nominal -1, -5/3, and -2 classes are not separated at any stated confidence level. With one run per parameter point and no bootstrap or synthetic-spectrum calibration, different reasonable window choices could move several peaks by several tenths and shift the regime boundaries in Fig. 7. The weakness is sharpened by the only run assigned to -5/3: the H-trap run at Omega/omega_perp = 0.95 has I = 2.39 and kint*xi ~ 0.8, which implies ell_int ~ 8 xi, not ell_int ~ xi as stated in Sec. 3(d). Thus the run does not meet the paper's own LLL conditions (I << 1, ell_int ~ xi). The qualitative differences between runs are plausible, but the sharp three-regime classification and the attribution of -5/3 to the LLL regime are not tightly supported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reviews the physics of rotating Bose-Einstein condensates and presents twelve new numerical simulations of the rotating Gross-Pitaevskii equation in harmonic, quartic, and box traps. On the basis of these simulations it proposes a three-regime classification of rotating quantum turbulence: a slowly rotating regime without a coherent vortex lattice, a rapidly rotating regime with a vortex lattice and an incompressible kinetic energy spectrum approximately k^-1, and a low Landau level regime near or above the trap frequency in which the spectrum softens to k^-5/3 or, at the most extreme parameters, k^-2. The paper also reviews existing experiments and simulations and uses weak-turbulence theory to rationalize the k^-1 and k^-2 exponents.","tokens_in":28549,"tokens_out":5232,"duration_ms":50064,"significance":"If the proposed classification survives closer statistical scrutiny it would be a useful organizing framework for a fragmented literature, and the comparison table of previous rotating quantum turbulence studies is a valuable contribution. The use of a public pseudospectral code, the explicit table of simulation parameters, and the attempt to tie spectral slopes to condensed-matter regimes (interaction parameter, LLL population) are strengths. However, the central quantitative claim rests on spectral exponents extracted from a small number of runs by visually selected fits, so the significance is currently potential rather than established.","major_comments":[{"comment":"The assignment of a spectral exponent alpha to each simulation is the load-bearing step in the three-regime classification, but the paper does not report any measure of uncertainty for alpha. The text states that wavenumber ranges are 'visually identified' and that the scaling exponent depends on k and t, and the insets of Figs. 4-6 show histograms whose counts span more than one unit in alpha. A bootstrap over the time window and over plausible wavenumber ranges, or synthetic spectra with known slopes, is needed to show that the -1, -5/3, and -2 classes are separated at a meaningful confidence level. Without this, the regime boundaries in Fig. 7 cannot be tested and the classification is not falsifiable from the reported data.","section":"Sec. 3(c), Fig. 7"},{"comment":"The only simulation assigned the LLL k^-5/3 exponent, the H-trap run with Omega/omega_perp=0.95, has I=2.39 and kint xi ~ 0.8. Since kint=2 pi/ell_int, this gives ell_int ~ 7.9 xi, not ell_int ~ xi, and I is not smaller than 1. The run therefore does not satisfy the paper's own criteria for the LLL regime stated in Sec. 2(d)(iii) and invoked in Sec. 3(d). Either additional simulations with I<<1 and ell_int ~ xi must be used to support the k^-5/3 attribution, or the paper should explicitly reformulate what signals approach to the LLL regime.","section":"Sec. 3(d), Fig. 4(d), Table 2"},{"comment":"The weak-turbulence interpretation is a post-hoc consistency check rather than an independent derivation. The parameters d, gamma, and N are chosen after the exponents have been measured, and the k^-5/3 case is not derived from Eq. (3.5) at all. To make the mechanism claim convincing, the authors should either apply Eq. (3.5) with parameters determined a priori from the identified wave modes (e.g., from spatio-temporal spectra), or present this material as a qualitative interpretation, not as a derivation of the observed exponents.","section":"Sec. 3(d), Eq. (3.5)"}],"minor_comments":[{"comment":"The sentence 'Table 2 summarizes many of these results' appears to refer to the literature summary table; Table 2 is the simulation parameter table. Please correct the cross-reference.","section":"Sec. 2(e)(ii)"},{"comment":"The phrase 'This motivated the pursue of obtaining a BEC' should read 'The pursuit of obtaining a BEC'.","section":"Sec. 2(a)"},{"comment":"The text contains the typo 'Thormas-Fermi approximation'; it should be 'Thomas-Fermi'.","section":"Sec. 2(d)(i)"},{"comment":"The phrase 'The total Hamiltonian for the condensate in the rotating frame them is' should read 'then is'.","section":"Sec. 2(c)"},{"comment":"The phrase 'reported by in 2017' contains an extra 'by'.","section":"Sec. 2(e)(ii)"},{"comment":"The word 'accesible' should be 'accessible'.","section":"Sec. 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of Phil. Trans. R. Soc. A, and the review portions are solid. The main issue is that the new quantitative claim needs stronger statistical support; I see this as correctable by additional analysis or by reframing the claims, rather than as a reason for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this if you want a compact map of where rotating quantum turbulence currently stands; the review half is genuinely useful. The new ingredient is a two-parameter regime map (Omega/omega_perp vs I) drawn from fresh 512^3 RGPE runs in harmonic, quartic and box traps, and the claim that the spectral slope of the incompressible energy splits into k^-1 (vortex lattice), k^-5/3 (approaching low Landau level), and k^-2 (extreme fast rotation). That organizing idea is plausible and fits the prior literature well; Table 1 alone is worth the download.\n\nThe soft spots are real and concentrated where the map is sharpest. Twelve runs, one per parameter point, and the spectral slopes are read from visually chosen k-ranges and broad histograms of the local logarithmic derivative. Insets in Figs 4-6 spread over more than one unit in alpha, so the three nominal classes are not separated at any stated confidence level. The weak-turbulence formula (3.5) is then tuned after the fact with gamma and N selected per regime, so it is an interpretation, not an independent test. The stress-test note lands: the only k^-5/3 case, H trap at Omega/omega_perp = 0.95, has I = 2.39 and kint*xi = 0.8, which gives ell_int ~ 8 xi, not the LLL condition ell_int ~ xi the text invokes. That particular point cannot carry the LLL attribution.\n\nNone of this sinks the paper. The qualitative regime distinction - lattice-dominated vs depleted-center vs strongly deformed - is visible in the density fields and in the energy evolution, and the comparison with previous experiments and simulations is careful, including a sensible warning about k^-3 artifacts. But the sharp three-regime classification and the k^-5/3 mapping to the LLL regime should be presented as hypotheses, not measured facts.\n\nI would send this to referees. The right referee instructions: ask for uncertainty quantification on the slopes, more runs near the claimed boundaries, release of the simulation parameters or data, and a rewrite of Sec. 3(d) that stops calling a post-hoc fit a derivation. I would not cite the specific exponents as established, but I would cite the parameter map and the literature table in my own work.","headline":"A useful review and a plausible regime map, but the sharp three-exponent classification rests on thin, visually fitted evidence and one k^-5/3 point that fails its own LLL test.","tokens_in":29072,"tokens_out":2147,"would_cite":true,"duration_ms":24310,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Rotating quantum turbulence is not one phenomenon but three regimes, each with its own kinetic-energy spectrum.","keywords":["rotating quantum turbulence","Bose-Einstein condensates","Gross-Pitaevskii equation","quantum vortex lattice","lowest Landau level","incompressible kinetic energy spectrum","Tkachenko waves","superfluid turbulence"],"falsifier":"Run a decaying rotating Gross-Pitaevskii simulation at fixed $\\Omega/\\omega_\\perp$ and $I$, and compute the incompressible kinetic energy spectrum over several non-overlapping time windows using automated wavenumber-range selection; if the histogram of local logarithmic derivatives no longer peaks near $-1$, $-5/3$, or $-2$, or if the peak shifts with the window, the claimed regime-specific scaling laws are not robust.","tokens_in":28020,"feed_emoji":"🌀","tokens_out":11627,"duration_ms":102689,"temperature":0.7,"pith_summary":"This paper tries to establish that the turbulence of a rotating superfluid is not a single phenomenon but a small set of distinct regimes, each with its own energy spectrum and dominant excitations. The organising parameters are the rotation rate relative to the trap, $\\Omega/\\omega_\\perp$, and the interaction strength $I$ that measures the population of the lowest Landau level. In the rapidly rotating regime, where a well-ordered vortex lattice forms, the incompressible kinetic energy spectrum scales roughly as $k^{-1}$; as the system approaches the lowest Landau level the spectrum becomes Kolmogorov-like, $\\sim k^{-5/3}$; and in extreme cases it steepens to $\\sim k^{-2}$. To support this map, the paper combines a review of experiments and simulations with twelve new numerical runs of the rotating Gross-Pitaevskii equation in harmonic, quartic, and box traps. A sympathetic reader would care because the three-regime picture reconciles previously scattered spectral exponents and says which parameters future experiments must report.","feed_headline":"Three regimes, three energy spectra, one rotating quantum flow","feed_subtitle":"Vortex-lattice, lowest-Landau-level, and slow-rotation states each show a different energy-spectrum slope.","key_machinery":"The load-bearing machinery is the rotating Gross-Pitaevskii equation, whose Hamiltonian gains the rotation term $-\\int \\psi^{*}\\boldsymbol{\\Omega}\\cdot\\boldsymbol{J}\\psi\\,d^3r$, together with two parameters that select the regime: $\\Omega/\\omega_\\perp$, the rotation rate relative to the trap, and $I=g\\rho_c/(2\\hbar m\\omega_\\perp)$, the interaction parameter measuring population of the lowest Landau level. The relevant structures are the Abrikosov vortex lattice (a triangular array of quantised vortices with inter-vortex spacing $\\ell_{\\rm int}\\approx 2\\sqrt{\\hbar/m\\Omega}$) and the healing length $\\xi$; when $\\ell_{\\rm int}\\gg \\xi$ the lattice survives and Tkachenko waves (collective oscillations of the lattice) carry the dynamics, and when $\\ell_{\\rm int}\\approx \\xi$ the lattice gives way to the low Landau level regime. The wave-turbulence formula $\\alpha = d-6+2\\gamma+(5-d-3\\gamma)/(N-1)$ converts the dispersion of soft Tkachenko waves ($\\gamma=2$, $N=4$ in $d=2$) into $\\alpha=-1$ and hard Tkachenko waves ($\\gamma=1$) into $\\alpha=-2$, providing a mechanistic origin for the observed spectral slopes.","core_discovery":"The central claim is that rotating quantum turbulence should be organised into three regimes: a slowly rotating regime in which no orderly vortex lattice develops and turbulence keeps features reminiscent of the isotropic case; a rapidly rotating regime in which an Abrikosov lattice of quantised vortices dominates and the incompressible kinetic energy spectrum is approximately $k^{-1}$; and a low Landau level regime near or above the trap frequency, where the condensate centre is depleted, vortices stretch near the edge, and the spectrum becomes approximately $k^{-5/3}$, or $k^{-2}$ in extreme cases. The authors show that the transition from $k^{-1}$ to $k^{-5/3}$ is tied to the inter-vortex distance approaching the healing length, $\\ell_{\\rm int}\\approx \\xi$, as quantified by a decreasing interaction parameter $I$. They also show that confinement matters: the same rotation rate that produces $k^{-5/3}$ in a harmonic trap returns to $k^{-1}$ in a quartic trap when the central density is restored, and small-$I$ quartic and box traps can produce $k^{-2}$ spectra.","pith_inferences":["A testable extension implicit in the paper: a fine scan of $I$ at fixed $\\Omega/\\omega_\\perp$ should reveal a sharp transition between $k^{-1}$ and $k^{-5/3}$ where $\\ell_{\\rm int}\\approx \\xi$, a boundary that could be located precisely by measuring the central density.","If the extreme-regime $k^{-2}$ spectrum is produced by inertial-wave interactions, rotating quantum gases could serve as controllable testbeds for classical rotating-turbulence scalings; if it comes from hard Tkachenko modes, the spatiotemporal spectrum should show the corresponding dispersion relation.","The shallow $k^{-1/2}$ spectrum seen in the low-density box trap may partly reflect the rigid wall rather than bulk physics; replacing the box by a softened wall in a follow-up simulation would separate boundary effects from genuine small-scale scaling.","The paper's regime map suggests experiments should report not only rotation rate but also the healing length and central density, since those determine $I$ and hence which spectral regime is being observed."],"forward_implications":["Reported spectra from very different stirring protocols—$k^{-1}$, $k^{-5/3}$, and $k^{-2}$—fall onto one map once $\\Omega/\\omega_\\perp$ and $I$ are known.","Approaching the lowest Landau level changes the turbulence mechanism: the vortex lattice dissolves, the condensate centre empties, and the spectrum becomes Kolmogorov-like.","The $k^{-1}$ scaling is tied to the vortex lattice and its collective motion, not to classical Kolmogorov cascading, so destroying the lattice should destroy that scaling.","Extreme rotation with weak interactions can produce $k^{-2}$ spectra, a regime the paper flags as needing further study because apparently similar published results come from different lattice states.","Rotating quantum fluids can serve as a bridge between turbulence theory and condensed matter physics, since rotation drives the system into distinct states of quantum matter rather than merely altering a cascade."],"supporting_citations":[{"why":"Provides the initial-condition method and the earlier three-dimensional RGPE results—$k^{-1}$ spectrum and inverse cascade—that this paper extends.","marker":"[13]"},{"why":"Establishes the slowly versus rapidly rotating behaviour, the split cascade, and relaxation to Abrikosov lattices used as a starting point.","marker":"[33]"},{"why":"Defines the slow, rapid, and lowest-Landau-level regimes and supplies the Thomas-Fermi radii and critical rotation formula used to classify runs.","marker":"[21]"},{"why":"Supplies the incompressible/compressible kinetic-energy decomposition and the single-vortex $k^{-1}$ spectrum behind Eq. (2.32).","marker":"[4]"},{"why":"Gives the lowest-Landau-level Hamiltonian and the mapping to a charged particle in a magnetic field, which defines the interaction parameter $I$.","marker":"[32]"},{"why":"A comparison simulation reporting $k^{-5/3}$ spectra under very fast stirring, cited as compatible with the lowest-Landau-level result.","marker":"[68]"},{"why":"A forced three-dimensional RGPE study reporting $k^{-2}$, used as the comparison and the flagged discrepancy for the extreme regime.","marker":"[71]"},{"why":"A two-dimensional RGPE study reporting $k^{-5/3}$ and $k^{-1}$ spectra, used to support the regime map across different stirring protocols.","marker":"[72]"},{"why":"Supplies the weak-turbulence scaling formula used to derive $\\alpha=-1$ for soft Tkachenko waves and $\\alpha=-2$ for hard ones.","marker":"[80]"}],"fun_headline_variants":["Rotating quantum turbulence: three regimes, three spectra","Three distinct spectra in rotating quantum turbulent flows","From vortex lattice to turbulence: rotation's three regimes","Quantum rotation: slow, fast, and extreme turbulent states","Mapping the three faces of rotating quantum turbulence"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The classification rests on reading clean power-law exponents from just twelve simulations, with visually chosen wavenumber ranges and a short time window; if different choices change the slopes, the sharp three-regime map is not established.","fun_headline_variants_meta":{"raw":{"variants":["Rotating quantum turbulence: three regimes, three spectra","Three distinct spectra in rotating quantum turbulent flows","From vortex lattice to turbulence: rotation's three regimes","Quantum rotation: slow, fast, and extreme turbulent states","Mapping the three faces of rotating quantum turbulence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000233,"raw_usage":{"total_tokens":1490,"prompt_tokens":936,"completion_tokens":554,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":481}},"tokens_in":552,"tokens_out":554,"duration_ms":5441,"temperature":1.0,"reasoning_tokens":481,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:27:34.240006+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a decaying rotating Gross-Pitaevskii simulation at fixed $\\Omega/\\omega_\\perp$ and $I$, and compute the incompressible kinetic energy spectrum over several non-overlapping time windows using automated wavenumber-range selection; if the histogram of local logarithmic derivatives no longer peaks near $-1$, $-5/3$, or $-2$, or if the peak shifts with the window, the claimed regime-specific scaling laws are not robust.","supporting_citations":[{"cited_title":"2022 Thermalized Abrikosov lattices from decaying turbulence in rotating BECs","cited_arxiv_id":null,"evidence_quote":"Establishes the slowly versus rapidly rotating behaviour, the split cascade, and relaxation to Abrikosov lattices used as a starting point."},{"cited_title":"2009 Rotating trapped Bose-Einstein condensates","cited_arxiv_id":null,"evidence_quote":"Defines the slow, rapid, and lowest-Landau-level regimes and supplies the Thomas-Fermi radii and critical rotation formula used to classify runs."},{"cited_title":"1997 Decaying Kolmogorov turbulence in a model of superflow","cited_arxiv_id":null,"evidence_quote":"Supplies the incompressible/compressible kinetic-energy decomposition and the single-vortex $k^{-1}$ spectrum behind Eq. (2.32)."},{"cited_title":"2008 Rotating trapped Bose-Einstein condensates","cited_arxiv_id":null,"evidence_quote":"Gives the lowest-Landau-level Hamiltonian and the mapping to a charged particle in a magnetic field, which defines the interaction parameter $I$."},{"cited_title":"2022 Vortex formation and quantum turbulence with rotating paddle potentials in a two-dimensional binary Bose-Einstein condensate","cited_arxiv_id":null,"evidence_quote":"A comparison simulation reporting $k^{-5/3}$ spectra under very fast stirring, cited as compatible with the lowest-Landau-level result."},{"cited_title":"2024 Emergence of isotropy in rotating turbulence of Bose-Einstein condensates","cited_arxiv_id":null,"evidence_quote":"A forced three-dimensional RGPE study reporting $k^{-2}$, used as the comparison and the flagged discrepancy for the extreme regime."},{"cited_title":"2024a Energy spectra and fluxes of turbulent rotating Bose–Einstein condensates in two dimensions","cited_arxiv_id":null,"evidence_quote":"A two-dimensional RGPE study reporting $k^{-5/3}$ and $k^{-1}$ spectra, used to support the regime map across different stirring protocols."}],"review_version":1}