Acoustic vortex beams in synthetic magnetic fields

Daniel Leykam; Irving Rondon

REVIEW 2 major objections 3 minor 29 references

Acoustic vortex beams in synthetic magnetic fields

T0 review · 2 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Rotating fluid acts as a magnetic field for sound vortex beams, splitting the response of pressure and velocity.

desk verdict 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. read the letter →

arxiv 1908.08278 v1 pith:OGN4QSWH submitted 2019-08-22 physics.class-ph

Irving Rondon , Daniel Leykam This is my paper · ORCID

classification physics.class-ph

keywords acousticvortexbeamssyntheticmagneticfieldspindensityAharonov-BohmfluxLaguerre-GaussBesselCouetteflowrotatingfluids

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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.

The 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.

The 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.

The 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.

My 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.

Referee Report

2 major / 3 minor

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.

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 (2)

[Sec. IIIA, Eqs. (23)-(27)] 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.
[Sec. II, Eq. (4) and Sec. IIIA] 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.

minor comments (3)

[Sec. IIIB, after Eq. (29)] 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.
[Eq. (22)] 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.
[Sec. IIIA, discussion after Eq. (25)] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the pressure/velocity asymmetries are derived from explicit exact solutions of the stated model, with no fitted parameters or load-bearing self-citations.

full rationale

The paper's derivation chain is self-contained and non-circular. It starts from the effective Schrödinger-type equation (4) for the acoustic velocity potential, obtained under explicitly stated weak-flow assumptions from prior acoustic literature; the target results are not used as inputs. The Laguerre-Gauss and Bessel solutions are standard exact solutions of the radial equations (23) and (28), and the subsequent field expressions (20)-(21) are direct definitions. Equations (26)-(27) for the pressure and longitudinal velocity densities are evaluations of |P|^2 = ρ^2(ω - u_θ l/r)^2 ψ^2 and |v_z|^2 = k_z^2 ψ^2 using the explicit dispersion relation (25); there is no parameter fitted to these profiles or to the claimed W-independence. The chosen cylinder radii and rotation speeds are illustrative operating points satisfying the stated validity constraints, not free parameters adjusted to force a conclusion. References to prior work, including the electron vortex beam formalism [22] and the acoustic vector-potential approximation [3,24], are external and are not self-citations by the present authors; no uniqueness theorem or ansatz is imported from the authors' own previous work. The skeptic's concern about the sign of the lΩ_2 term in Eq. (25) is a possible correctness or calculation error and would affect the validity of the uniform-field claim, but it is not circularity: the dispersion relation is an explicitly solved input, not a hidden restatement of the pressure/velocity asymmetry it is used to explain.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claims depend on the approximate Schrödinger equation, the assumed Couette flow, and the Neumann boundary condition, all of which are standard or explicitly stated. No new physical entities are introduced. The illustrative parameter values are chosen to satisfy validity constraints, not fitted to data.

free parameters (5)

Omega_2/omega = 0.005
Outer cylinder rotation rate relative to acoustic frequency for the uniform-field case; chosen so that the peak fluid speed u_max = 0.2c satisfies the weak-flow condition and R_2 > beam waist.
R_2 omega/c = 40
Outer cylinder radius; chosen with Omega_2 to place the system in the Goldilocks zone where the Laguerre-Gauss beam is localized by the synthetic field and the flow is slow.
Omega_1 = 0.02 (in units omega=1)
Inner cylinder angular speed for the Aharonov-Bohm flux case; chosen together with R_1=5 to give flux alpha=1/2 while keeping u_max=0.1c small.
R_1 = 5 (in units c/omega)
Inner cylinder radius for the flux tube; large slowly rotating inner cylinder maximizes flux under the weak-flow constraint.
beam angle phi = pi/8
Moderately non-paraxial angle for Bessel beams, chosen to maximize vector-potential effects while keeping the beam within the validity regime of the scalar equation.

assumptions (6)

domain assumption Acoustic wave equation in a moving fluid, Eq. (1), with D_t = partial_t + u dot grad, from Refs. [3,24].
This is the standard model for small-amplitude sound in a steadily moving incompressible fluid; the paper does not derive it.
domain assumption The effective Schrödinger equation (4) with vector potential A = -omega u/c^2 is valid when u^2/c^2 << 1 and u varies slowly compared with the acoustic wavelength.
This approximation is load-bearing for all mode solutions in Sec. III; the paper states it but does not quantify the error.
domain assumption Couette flow profile (22) between concentric rotating cylinders, including stability limit against Taylor instabilities.
The flow profile is taken from fluid mechanics [23]; the stability constraint restricts accessible synthetic magnetic fields.
domain assumption Hard-wall Neumann boundary condition partial_r psi(R_1,2) = 0 for the velocity potential at the cylinder walls.
Used to select the Bessel mode coefficients in Eqs. (30) and (32).
standard math Definitions of energy, canonical momentum, spin, and angular momentum densities from the four-component acoustic wavefunction in Ref. [13].
These definitions are imported from prior work and used to compute observables.
standard math Standard properties of Laguerre polynomials and Bessel functions, including linear dependence of J_n and J_{-n} for integer orders.
Used to write the LG modes and the integer-flux Bessel solution.

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Cite this review

Pith. "Pith review of Acoustic vortex beams in synthetic magnetic fields." pith.science (2026). https://pith.science/paper/OGN4QSWH

@misc{pith2026190808278,
  author       = {Pith},
  title        = {Pith review of: Acoustic vortex beams in synthetic magnetic fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OGN4QSWH}},
  note         = {Machine review of arXiv:1908.08278}
}

read the original abstract

We analyze propagation of acoustic vortex beams in longitudinal synthetic magnetic fields. We show how to generate two field configurations using a fluid contained in circulating cylinders: a uniform synthetic magnetic field hosting Laguerre-Gauss modes, and an Aharonov-Bohm flux tube hosting Bessel beams. For non-paraxial beams we find qualitative differences from the well-studied case of electron vortex beams in magnetic fields, arising due to the vectorial nature of the acoustic wave's velocity field. In particular, the pressure and velocity components of the acoustic wave can be individually sensitive to the relative sign of the beam orbital angular momentum and the magnetic field. Our findings illustrate how analogies between optical, electron, and acoustic vortex beams can break down in the presence of external vector potentials.

Figures

Figures reproduced from arXiv: 1908.08278 by the authors.

**Figure 2.** FIG. 2: Phase diagram of acoustic vortex beams supported [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3: Pressure [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4: Normalised transverse spin [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: plots P, v, and W profiles of the acoustic Bessel beams. The synthetic flux α strongly breaks the symmetry between beams with orbital angular momentum ±l; the beam radius is larger when sgn(αl) > 0. While beams with the same |l+α| have identical velocity potentials ψ,…

**Figure 6.** Figure 6: plot some other observables. The transverse Sθ and longitudinal Sz spin densities become large close to the minima of W. In this non-paraxial regime, the peak values of Sz/W are sensitive to the enclosed flux α. The longitudinal momentum Πz is determined purely by |l +…

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010)

2010

[2] [2]

Ozawa, H

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zil- berberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019)

2019

[3] [3]

Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. D. Chong, and B. Zhang, Topological acoustics, Phys. Rev. Lett. 114, 114301 (2015)

work page 2015

[4] [4]

H. Ge, X. Ni, Y. Tian, S. K. Gupta, M.-H. Lu, X. Lin, W.-D. Huang, C. T. Chan, and Y.-F. Chen, Experimen- tal observation of acoustic Weyl points and topological surface states, Phys. Rev. Appl. 10, 014017 (2018)

work page 2018

[5] [5]

S. Wang, G. Ma, and C. T. Chan, Topological transport of sound mediated by spin-redirection geometric phase , Science Adv. 4, eaaq1475 (2018)

work page 2018

[6] [6]

G. Ma, M. Xiao, and C. T. Chan, Topological phases in acoustic and mechanical systems , Nature Rev. Phys. 1, 281 (2019)

work page 2019

[7] [7]

D. L. Andrews and M. Babiker, The Angular Momentum of Light, Cambridge University Press (2013)

work page 2013

[8] [8]

K. Y. Bliokh, I. P. Ivanov, G. Guzzinati, L. Clark, R. Van Boxem, A. Beche, R. Juchtmans, M. A. Alonso, P. Schattschneider, F. Nori, and J. Verbeeck, Theory and applications of free-electron vortex states , Physics Re- ports 690, 1 (2017)

work page 2017