{"id":"9f85e788-c057-47d0-ba5d-b51b91543cd2","arxiv_id":"1908.08278","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":5,"one_line_summary":"Acoustic vortex beams in rotating-fluid waveguides feel a synthetic magnetic field, and their pressure and velocity components respond differently to the relative sign of beam angular momentum and field, unlike scalar electron beams.","lead":"This paper analyzes how acoustic vortex beams propagate in a rotating fluid that creates a synthetic magnetic field for sound. It shows that a beam's pressure and velocity fields can react differently to the direction of rotation, a vectorial effect that electron vortex beams do not exhibit.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sign error in Eq. (25) appears to invalidate the claimed W-independence in the uniform-field case.","rationale":"The Reader's weakest assumption concerned the validity of the approximate Schrödinger equation (4). That approximation is a legitimate and clearly flagged limitation, and I would not make it the decisive issue. The more serious problem is internal: Eq. (25) is inconsistent with Eq. (23) by an algebraic sign. Because the uniform-field demonstration is built on this dispersion relation, the specific headline claim that W remains insensitive to sgn(lΩ2) is not supported. The check is purely analytic and decisive: substituting the stated LG solution into the stated radial equation gives a different dispersion. I do not question the Bessel/AB section, which may survive, but the abstract's central example and the reader's strongest claim fail as written. This warrants rejection of the current version rather than acceptance.","tokens_in":10128,"tokens_out":27264,"duration_ms":285447,"concrete_test":"Recompute kz for the n=0, l=±1 Laguerre-Gauss modes by substituting Eq. (24) directly into Eq. (23) and solving the resulting algebraic eigenvalue equation, without using Eq. (25). If the l=+1 mode gives (ckz/ω)² = 1 - 6Ω2/ω and the l=-1 mode gives 1 - 2Ω2/ω (for Ω2>0), then Eq. (25) has the wrong sign. Then evaluate W from Eqs. (5), (20), and (21) with the corrected kz; if W(l=+1) differs from W(l=-1) at order Ω2/ω, the claimed W-independence and the associated qualitative conclusion for uniform fields are false.","verdict_should_be":"REJECT","load_bearing_attack":"The central advertised result for Sec. IIIA is that the total energy density W is insensitive to sgn(lΩ2) while P and vz are individually sensitive (Eqs. (26)-(27), Fig. 3). This cancellation rests entirely on the sign of the lΩ term in the dispersion relation (25). Direct substitution of the stated Laguerre-Gauss solution (24) into the radial equation (23) gives the opposite sign. For example, take n=0, l=1, Ω2>0, with ψ=(r/w)e^{-r²/w²} and w²=2c²/(ωΩ2). Writing β=ωΩ2/c², the operator in Eq. (23) acting on ψ yields (1/r²+β²r²+2β)ψ minus the radial Laplacian, whose eigenvalue is 6β, not 2β. Hence (ckz/ω)² = 1 - 6Ω2/ω, whereas Eq. (25) gives 1 - 2Ω2/ω. Repeating for l=-1 gives (ckz/ω)² = 1 - 2Ω2/ω. Thus Eq. (25) has the lΩ term with the wrong sign, and Eq. (27), which is built on it, has the opposite lΩ dependence from the correct kz². With the correct dispersion, the lΩ terms in |P|² and |vz|² do not cancel in W: both contribute with the same sign at first order in Ω/ω, so W is not independent of sgn(lΩ2). The uniform-field central claim is therefore not established.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies acoustic vortex beams propagating through a fluid with a background azimuthal flow that acts as a synthetic vector potential. The authors derive an effective Schrödinger-like equation for the velocity potential, analyze two cylindrical geometries (a uniform synthetic magnetic field supporting Laguerre-Gauss modes and a synthetic Aharonov-Bohm flux tube supporting Bessel beams), and compute the acoustic pressure, velocity, energy, spin, and momentum densities. The main advertised finding is that, for non-paraxial beams, the individual pressure and velocity components are sensitive to the relative sign of the beam orbital angular momentum and the synthetic magnetic field, even when the total energy density is not, illustrating a qualitative difference from scalar electron vortex beams.","tokens_in":10460,"tokens_out":22364,"duration_ms":210935,"significance":"The paper is clearly written and the analytical framework is attractive: it connects acoustic vortex beams to the well-developed formalism of electron beams in magnetic fields and aims to expose genuine vectorial effects of acoustic fields. The Aharonov-Bohm flux-tube analysis, in particular, appears self-contained and yields concrete predictions for flux-dependent spin and momentum densities. The strengths are the explicit derivations and the care taken to state the validity constraints on the background flow. However, the uniform-field section contains a sign error in the dispersion relation that undermines the central claim of energy-density independence from the sign of the product lΩ2. Since this claim is highlighted in the introduction, figure captions, and conclusions, the paper cannot be accepted in its current form. The error is correctable by revision, and the remaining formalism and AB analysis may form a solid basis for a revised manuscript.","major_comments":[{"comment":"Equation (25) has the wrong sign for the lΩ2 term. Direct substitution of the n=0, l=1 Laguerre-Gauss mode ψ = (r/w)e^{-r²/w²} with w² = 2c²/(ωΩ2) into Eq. (23) for Ω2 > 0 yields the eigenvalue (ω²/c² - 6ωΩ2/c²)ψ, so (ckz/ω)² = 1 - 6Ω2/ω, whereas Eq. (25) gives 1 - 2Ω2/ω. Repeating for l = -1 gives (ckz/ω)² = 1 - 2Ω2/ω, not 1 - 6Ω2/ω. The correct dispersion is (ckz/ω)² = 1 - 2lΩ2/ω - 2|Ω2|/ω(2n+|l|+1). Consequently Eq. (27) carries the wrong sign in its lΩ2 term: with the correct kz², the lΩ2 terms in β|P|² and ρ|vz|² add rather than cancel, and W is sensitive to sgn(lΩ2). The claimed W-independence in the text and in Fig. 3 is therefore not established. This is a load-bearing error for the uniform-field section.","section":"Sec. IIIA, Eqs. (23)-(27)"},{"comment":"The paper states that Eq. (4) follows from Eq. (1) under u²/c² << 1, but Eq. (4) retains the |A|² term while dropping the (u·∇)² term. For the uniform-flow profile u = Ω2 r eθ these two terms are of different parametric order: at the beam waist, |A|² contributes at order Ω2/ω to the dispersion relation, whereas (u·∇)² = -(lΩ2)² is of order (Ω2/ω)². Since the localization of the Laguerre-Gauss modes and the l-dependent cutoff in Eq. (25) rely on the |A|² term, the paper should explicitly state the ordering that justifies retaining this term while neglecting (u·∇)². As written, the derivation of Eq. (4) is presented as a direct recasting and leaves this point unclear.","section":"Sec. II, Eq. (4) and Sec. IIIA"}],"minor_comments":[{"comment":"The numerical values Ω1 = 0.02 and R1 = 5 are quoted without units; since the figures use rω/c as the radial unit, please state R1 in units of c/ω and Ω1 in units of ω.","section":"Sec. IIIB, after Eq. (29)"},{"comment":"The typeset expression for the Couette flow profile is difficult to parse; please check the spacing and parentheses so that the two terms in Eq. (22) are unambiguous.","section":"Eq. (22)"},{"comment":"Once the sign in Eq. (25) is corrected, the sentence describing the l-dependent modal cutoff should be revisited, since the condition for guided modes depends on the corrected dispersion.","section":"Sec. IIIA, discussion after Eq. (25)"}],"recommendation":"major_revision","confidential_remarks":"The sign error in Eq. (25) is decisive: it reverses the advertised lΩ2 dependence and invalidates the W-independence claim. I recommend major revision rather than rejection because the Aharonov-Bohm section and the general vectorial formalism appear sound and could form the basis of a corrected paper. However, the revision must confront the corrected uniform-field dispersion honestly; if the authors cannot revise the uniform-field claims, rejection would be the appropriate outcome."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the uniform-field half of this paper is wrong in a way that kills its main advertised result; the Aharonov-Bohm half appears sound. Referee it, but expect a major revision.\n\nThe new thing here is the idea of putting acoustic vortex beams in a rotating-fluid synthetic gauge field and looking at the vectorial acoustic spin/momentum densities rather than just the Schrödinger-potential description. The derivations are explicit and the Bessel beam part (Sec. IIIB) is a clean calculation: the flux α shifts the Bessel order to l+α, and the spin/energy profiles show a real sign-sensitivity that isn't in the earlier free-space acoustics papers.\n\nThe problem is Sec. IIIA. Equation (25) has the wrong sign on the lΩ2 term. I checked by substituting their stated LG solution ψ=(r/w)e^{-r²/w²} into their radial equation (23). For n=0, l=1, Ω2>0, the operator gives an eigenvalue ω²/c² - 6β, not ω²/c² - 2β as Eq. (25) claims (β=ωΩ2/c²). The correct dispersion has (ckz/ω)² = 1 - 2lΩ2/ω - 2|Ω2|/ω(2n+|l|+1). The sign on the l-dependent term is flipped relative to Eq. (25). This is not a cosmetic typo: the advertised cancellation in W between |P|² and |vz|² disappears. With the correct sign the lΩ2 terms add, so the total energy density W depends on sgn(lΩ2). Figure 3 as drawn is therefore wrong.\n\nThe physical origin is easy to state: for a wave in a medium moving azimuthally the local frequency is Doppler-shifted down, ω - lΩ, not up. Equation (25) effectively uses ω + lΩ. The authors likely imported the electron-vortex dispersion without adjusting for the charge-sign convention in their acoustic analogy.\n\nThe Bessel section doesn't share this flaw; there the gauge field enters as an integer shift l+α in the Bessel order, which is derivationally clean. So the paper has a salvageable core. But the uniform-field section is load-bearing for the abstract's central claim about W being insensitive to sgn(lΩ2). As is, that claim is false.\n\nMy take: this should go to an expert referee, not be desk rejected, but it should come back with a major-revision request. The authors need to correct the dispersion and all downstream results (Eqs. (26)-(27), Figs. 3-4), and either drop or substantially revise the W-independence claim. Once that's done, the Bessel part plus the corrected uniform-field analysis could be a solid paper.","headline":"The uniform-field central claim fails on a sign error in Eq. (25); the Bessel-beam half survives and the paper deserves a referee but with major revisions.","tokens_in":10951,"tokens_out":22500,"would_cite":false,"duration_ms":180191,"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 fluid acts as a magnetic field for sound vortex beams, splitting the response of pressure and velocity.","keywords":["acoustic vortex beams","synthetic magnetic field","acoustic spin density","Aharonov-Bohm flux","Laguerre-Gauss beams","Bessel beams","Couette flow","rotating fluids"],"falsifier":"Measure, in a Couette-flow waveguide, the pressure and velocity profiles of Bessel beams with orbital angular momentum l and -l at fixed cylinder rotation, in the moderately non-paraxial regime. The paper predicts the beam radius shifts with sgn(αl) and the peak spin density S_z/W changes sign and magnitude with α; observing no such asymmetry, or finding that W depends on sgn(lΩ), would falsify the central claim.","tokens_in":9939,"feed_emoji":"🌀","tokens_out":4289,"duration_ms":41683,"temperature":0.7,"pith_summary":"This paper argues that acoustic vortex beams—sound beams carrying orbital angular momentum—can be made to feel a synthetic magnetic field by passing through a fluid that rotates between concentric cylinders. Under uniform rotation, the beam takes Laguerre-Gauss form; under a thin inner vortex, it becomes a Bessel beam threaded by an Aharonov-Bohm flux. Because sound has both a pressure field and a vector velocity field, the beam's pressure and velocity components respond separately to whether the beam's orbital angular momentum is aligned or anti-aligned with the synthetic field, even though the total energy density does not. The paper's point is that the familiar analogy with electron vortex beams in real magnetic fields breaks down in a useful way: the vectorial nature of sound gives experimental access to the sign of the field-beam interaction.","feed_headline":"Rotating fluid acts as a magnetic field for sound vortex beams","feed_subtitle":"Pressure and velocity of the beam respond separately to the field's direction, a vector effect electron beams lack.","key_machinery":"The central object is the four-component acoustic wavefunction |Ψ⟩ = (P, v)ᵀ and the coupled first-order equations for pressure and velocity, rather than the scalar velocity-potential equation alone. The load-bearing identity is the kinetic momentum decomposition Π/c² = p + (1/4)∇×S - (W/ω)A, with spin density S = (ρ/2ω) Im(v* × v). This identity makes the vectorial effects visible: the ∇×S term suppresses the longitudinal kinetic momentum near vortex cores, and the W A term couples momentum to the background flow. The two exact solution families—Laguerre-Gauss modes for a uniform synthetic field and Bessel beams for a synthetic flux tube—carry the paper's concrete predictions.","core_discovery":"The paper shows that in a background flow u much slower than the sound speed c, the acoustic velocity potential obeys an effective Schrödinger equation with vector potential A = -ω u/c². In a cylindrical waveguide filled with Couette flow, two exact mode families solve this equation. A uniform synthetic field gives Laguerre-Gauss beams whose dispersion contains the Zeeman-like term 2lΩ₂/ω. The modal profiles and total energy density W are independent of sgn(lΩ₂), but the pressure density |P|² and the longitudinal velocity density |v_z|² shift in opposite directions, so a detector sensitive only to one field component can register the relative sign of orbital angular momentum and field. For an Aharonov-Bohm flux line, the Bessel beam solutions have velocity potential determined by l+α, yet the pressure, velocity, and energy profiles depend on l and α separately; the flux tunes both the beam radius and the magnitude and sign of the acoustic spin density. The paper concludes that synthetic magnetic fields provide a new control handle on acoustic spin and local momentum densities, with effects that are invisible in the scalar Schrödinger picture.","pith_inferences":["A differential measurement of |P|² and |v_z|² could act as a compact rotation-direction sensor in fluids, since the two components shift oppositely with sgn(lΩ₂).","The same formalism suggests that acoustic surface waves in rotating fluids should exhibit unidirectional propagation and spin-momentum locking, extending the waveguide analysis to open geometries.","The flux-dependent spin density might be exploitable for acoustic tweezers, as radiation forces on small particles couple to momentum and spin densities.","A concrete testable extension: measure the beam radius and spin density of a non-paraxial Bessel beam while reversing the cylinder rotation direction; the paper's formalism predicts the radius increases for sgn(αl) > 0 relative to sgn(αl) < 0."],"forward_implications":["A pressure-only detector and a velocity-sensitive probe would observe different sign-dependent shifts for the same acoustic vortex beam in a rotating-fluid waveguide.","The Aharonov-Bohm flux provides a continuous knob for the beam radius and for the sign and magnitude of the longitudinal spin density, not just for the phase of the wavefunction.","Synthetic magnetic fields allow spin and kinetic momentum densities to be controlled near zeros of the pressure field, where canonical and spin momentum point in opposite directions.","Because the total energy density is sign-insensitive while the component densities are not, measurements of W alone cannot reveal the sign of the field-beam interaction.","The comparison with electron vortex beams shows that vectorial field structure can break otherwise robust analogies between optical, electron, and acoustic waves."],"supporting_citations":[{"why":"Supplies the quantum-like formalism for acoustic spin and canonical momentum that the paper extends to a background vector potential.","marker":"[13]"},{"why":"Provides the electron vortex beam comparison and the Laguerre-Gauss and Aharonov-Bohm solution families that the acoustic analysis is modeled on.","marker":"[22]"},{"why":"Supplies the effective Schrödinger equation for sound in moving fluid and the Taylor-instability constraint on flow speed.","marker":"[3]"},{"why":"Provides the Aharonov-Bohm analogue for waves in circulating flow that motivates the acoustic flux-tube configuration.","marker":"[20]"},{"why":"Gives the Couette flow background and the stability threshold that limits the accessible synthetic-field strengths.","marker":"[23]"},{"why":"Supplies the wave equation for sound in unsteady inhomogeneous flow from which the effective vector-potential description is derived.","marker":"[24]"}],"fun_headline_variants":["Sound vortex beams sense magnetic fields made of moving fluid","Acoustic vortices reveal vector effects hidden from electron beams","Rotating fluid creates magnetic field for acoustic vortex beams","Pressure and velocity of sound vortices respond separately to field","Synthetic magnetic fields twist acoustic vortex beams"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The results rest on the approximation that the background flow is slow and slowly varying compared with the sound wave, so that the acoustic field obeys the effective Schrödinger equation with neglected terms of order (u/c)² and gradient corrections; if those terms matter for the moderately non-paraxial beams, the predicted component asymmetries could be modified.","fun_headline_variants_meta":{"raw":{"variants":["Sound vortex beams sense magnetic fields made of moving fluid","Acoustic vortices reveal vector effects hidden from electron beams","Rotating fluid creates magnetic field for acoustic vortex beams","Pressure and velocity of sound vortices respond separately to field","Synthetic magnetic fields twist acoustic vortex beams"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000645,"raw_usage":{"total_tokens":2937,"prompt_tokens":891,"completion_tokens":2046,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":1970}},"tokens_in":507,"tokens_out":2046,"duration_ms":13163,"temperature":1.0,"reasoning_tokens":1970,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:45:03.296366+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure, in a Couette-flow waveguide, the pressure and velocity profiles of Bessel beams with orbital angular momentum l and -l at fixed cylinder rotation, in the moderately non-paraxial regime. The paper predicts the beam radius shifts with sgn(αl) and the peak spin density S_z/W changes sign and magnitude with α; observing no such asymmetry, or finding that W depends on sgn(lΩ), would falsify the central claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the quantum-like formalism for acoustic spin and canonical momentum that the paper extends to a background vector potential."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the electron vortex beam comparison and the Laguerre-Gauss and Aharonov-Bohm solution families that the acoustic analysis is modeled on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the effective Schrödinger equation for sound in moving fluid and the Taylor-instability constraint on flow speed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Aharonov-Bohm analogue for waves in circulating flow that motivates the acoustic flux-tube configuration."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the Couette flow background and the stability threshold that limits the accessible synthetic-field strengths."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the wave equation for sound in unsteady inhomogeneous flow from which the effective vector-potential description is derived."}],"review_version":1}