Pith. sign in

REVIEW 3 major objections 4 minor 118 references

Electrodynamics of Vortices in Quasi-2D Scalar Bose-Einstein Condensates

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Vortices in a quasi-2D scalar BEC can be mapped onto a set of effective Maxwell equations that hold even for inhomogeneous, time-dependent condensates with dissipation or rotation.

desk verdict Clever dictionary, missing derivation: the central Ampere–Maxwell analog assumes an unproved Euler equation for the pseudo-velocity, so the general duality doesn't hold as stated. read the letter →

arxiv 2411.14302 v4 pith:2WH3HHCH submitted 2024-11-21 cond-mat.quant-gas cond-mat.stat-mechmath-phmath.MPphysics.plasm-phquant-ph

Seong-Ho Shinn , Adolfo del Campo This is my paper · ORCID
classification cond-mat.quant-gascond-mat.stat-mechmath-phmath.MPphysics.plasm-phquant-ph
keywords Bose-EinsteincondensatevortexdynamicseffectiveMaxwellequationsdualitypoint-vortexmodelsuperfluidtwo-dimensionalelectrodynamicsGross-Pitaevskiiequation
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

Vortices in a quasi-two-dimensional scalar Bose-Einstein condensate can be described as electric charges in an effective two-dimensional electrodynamics. Starting from the Gross-Pitaevskii equation, the paper derives a set of effective Maxwell equations that hold even when the condensate density is inhomogeneous and time dependent, and it extends the mapping to dissipative dynamics and to rotating condensates, beyond the usual point-vortex approximation. The payoff is a common language for vortex motion, vortex creation and annihilation, and vortex-vortex interactions: quantities like charge, current, field, radiation, and the Poynting vector get concrete geometric meanings in the superfluid. If the duality is correct, standard electromagnetic intuition can be brought to bear on vortex patterns in quenched or stirred condensates.

What carries the argument

The load-bearing construction is the pseudo-superfluid velocity $v_P(r,t)$, defined only through its curl, together with the effective fields $E_{sf}$, $D_{sf}$, $P_{sf}=D_{sf}-\epsilon_{sf}E_{sf}$, and $H_{sf}$ built from $v_P$, the actual superfluid velocity $v_s$, and the effective potential $U_{sf}=V+gn$. The curl relation fixes the vortex charge density $\rho_v$, and the difference field $P_{sf}$ tracks deviations from the point-vortex model. The identification of $H_{sf}$ with the spatially averaged effective potential turns the Euler equation into an Ampere-Maxwell law, while the Faraday analog is manufactured by defining a magnetic current $J_{m,sf}$ that automatically satisfies its own continuity equation. The effective speed of light is identified with the maximum speed of sound, $c_{sf}=c_s=\sqrt{g n_{\mathrm{max}}/M}$.

What would settle it

A direct numerical test would solve the Gross-Pitaevskii equation for a single vortex moving through an inhomogeneous background, extract $n$ and $v_s$, compute $D_{sf}$, $H_{sf}$, and $J_{sf}$ via the paper's definitions, and check whether the Ampere-Maxwell equation holds at each time step; a mismatch at the order of $\partial P_{sf}/\partial t$ would falsify the general duality and reveal the needed correction.

Watch

Extended reading notes

Core claim

The paper's central claim is that, once one introduces a pseudo-superfluid velocity $v_P$ by $\nabla\times v_P = e_\perp (2\pi\hbar/M)\sum_j q_j(t)\,\delta(r-r_j(t))$ and defines effective fields $D_{sf} = (M/2\pi\hbar)\, v_s\times e_\perp$, $E_{sf} = (M/2\pi\hbar\epsilon_{sf})\, v_P\times e_\perp$, and $H_{sf} = -(U_{sf}-\bar U_{sf})\,e_\perp/(2\pi\hbar)$, the vortex dynamics is exactly enclosed by the four equations $\nabla\cdot D_{sf}=\rho_v$, $\nabla\times H_{sf}=J_{sf}+\partial D_{sf}/\partial t$, $\nabla\cdot H_{sf}=0$, and $c_{sf}^2\nabla\times D_{sf}=-J_{m,sf}-\partial H_{sf}/\partial t$. These equations are claimed to hold beyond the point-vortex model, with inhomogeneous and time-dependent density, and in rotating or dissipative systems. From them the paper derives an effective Lorentz force on a vortex, an effective Poynting vector parallel to the pseudo-superfluid velocity, a generalized damped point-vortex model, and formulas for the time rate of change of the circulation.

Load-bearing premise

The load-bearing premise is that an auxiliary velocity field $v_P$, defined only by the requirement that its curl concentrates at vortex cores, moves according to the same Euler-type equation as the real superfluid velocity; no proof of that equation for $v_P$ is given, and the alternative of a time-independent effective polarization also goes unproven beyond the point-vortex model.

Editorial extensions

If this is right

  • Vortex patterns in quenched or stirred quasi-2D condensates can be simulated or interpreted with the vocabulary of electrodynamics: vortex charges, effective currents, and fields, including regimes where the point-vortex model fails.
  • The damped point-vortex model emerges as a special case of the effective Lorentz force, so dissipation-driven vortex annihilation and mutual friction acquire a field-theoretic description.
  • In the homogeneous, nonrotating point-vortex limit, the known logarithmic vortex interaction and 2D Coulomb gas behavior are recovered, and the BKT transition temperature in the GPE+PVM description is $T_c = n\pi\hbar^2 Q^2/(2M k_B)$.
  • When vortices move, the logarithmic interaction receives corrections of order $|r-r_\alpha(t)|^2/(c_{sf}t)^2$ in the near-field approximation, traceable to effective Liénard-Wiechert potentials in 2+1 dimensions.
  • Vortex charge conservation is not assumed; the continuity equation for the vortex charge delivers a formula for the rate of change of circulation in a static area, with phonon emission implicated in vortex creation and annihilation.

Reading between the lines

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

  • An unstated consequence is that vortex-antivortex annihilation in a quasi-2D BEC should emit a burst of sound whose angular and frequency content mirrors the effective electromagnetic radiation of annihilating charges; a vortex collider experiment could look for this signature.
  • The derivation suggests the duality is exact only when the effective polarization obeys $\partial P_{sf}/\partial t=0$ or when $v_P$ obeys the same Euler equation as $v_s$; for finite-size vortex cores these conditions fail, so a modified set of equations with residual source terms likely governs real condensates.
  • The same construction should apply to defects other than vortices, e.g., dislocations in 2D solids or skyrmions in spinor condensates, whenever the defect charge can be encoded in the curl of a velocity-like field; the paper gestures at this but does not develop it.
  • If the effective Poynting vector indeed controls vortex energetics, then vortex drift in inhomogeneous or rotating traps could be interpreted as effective radiation pressure, which may offer a new diagnostic for vortex dynamics in experiments.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper claims to establish a general duality between vortices in a quasi-2D scalar Bose-Einstein condensate and effective 2D electrodynamics, going beyond the point-vortex model to inhomogeneous, time-dependent condensate density, dissipation, and rotation. Starting from the Gross-Pitaevskii equation (and a generalized dissipative/rotating extension), the authors define effective electric and magnetic fields, polarization, currents, and potentials, and assert the effective Maxwell equations in Table III: Eqs. (39), (46), (47), and (50). They then use this duality to discuss an effective Poynting vector, retarded potentials, the damped point-vortex model, vortex stability, and the temporal change of circulation.

Significance. If the central derivation were correct, this would be a valuable unification, extending earlier vortex-electrodynamics dualities that assume uniform or time-independent density to a broader class of situations, including vortex creation and annihilation. The paper is ambitious, clearly structured, and contains useful discussions of vortex charge non-conservation and the rotating-frame case (Appendix A). However, the key step leading to the Ampere-Maxwell analog contains a missing polarization-current term, and much of the remaining structure is definitional. The claimed generality beyond the point-vortex model is therefore not established.

major comments (3)
  1. [Sec. IV, Eq. (43)] The derivation of Eq. (43) is incorrect. Direct substitution of Eqs. (22), (36), (38), and (41) into the time derivative of D_sf gives ∂D_sf/∂t = -J_sf + ∇×(-U_sf/(2πℏ) e_⊥) - ∂P_sf/∂t. The term -∂P_sf/∂t is absent in Eq. (43). Consequently, Eq. (46), ∇×H_sf = J_sf + ∂D_sf/∂t, holds only when ∂P_sf/∂t = 0. Since P_sf measures the deviation from the point-vortex model and is generally time-dependent for inhomogeneous, time-dependent condensates, the claimed Ampere-Maxwell analog is not valid beyond the PVM. This error is load-bearing: it propagates to the retarded-potential solution (Eq. (56)) and to the damped-PVM discussion in Sec. V, both of which rely on Eq. (46).
  2. [Sec. IV, Eqs. (36)-(38) and (41)] The equality in Eq. (43) requires the pseudo-superfluid velocity v_P to satisfy M ∂v_P/∂t = f_K + F_sf - ∇U_sf, the same Euler equation as the true superfluid velocity v_s. However, v_P is defined only through its curl in Eq. (37), with no equation of motion or initial condition specified. Using the actual equation for v_s (Eq. (22)) yields the discrepancy -∂P_sf/∂t noted above. Thus the derivation of the Ampere-Maxwell analog relies on an unstated and unjustified dynamical assumption about v_P.
  3. [Sec. IV, Table III] The claimed 'derivation' of the effective Maxwell equations is largely definitional. Equation (39) is an identity following from the definitions of D_sf and ρ_v; Eq. (50) is made true by the definition of J_m,sf in Eq. (49); and Eq. (47) is automatic in two dimensions because H_sf ∝ e_⊥. The only equation with nontrivial content, Eq. (46), is the one that fails. Moreover, the vortex quantization condition (Eq. (30)) fixes ∇×v_s to a sum of delta functions, so ∇·D_sf = ρ_v forces ρ_v = Σ_j q_j δ(r - r_αj) and ∇·P_sf = 0. The claimed extension 'beyond the PVM' is therefore not realized in the present treatment; the polarization P_sf does not modify the charge density, and its time derivative is exactly the term missing from the Ampere-Maxwell analog.
minor comments (4)
  1. [Sec. V, Eq. (60)] In Eq. (60), the last term involves ∂P_sf(t)/∂t, but P_sf depends on both r and t; this should read ∂P_sf(r,t)/∂t.
  2. [Sec. VI, Eq. (64)] The notation 'dl e_n · J_sf' in the first line of Eq. (64) is confusing; the line integral should be written as ∮ dl · J_sf or with explicit components, and the orientation should be specified.
  3. [Sec. IV, Eq. (35)] The definition of ρ_v in Eq. (35) fixes only its integral over the region A. The local value is determined by Eq. (39) (via ∇·D_sf), but this is not stated explicitly; the text should clarify that ρ_v is not an independent free field.
  4. [Sec. V, after Eq. (60)] The assumption P_sf(r,t) ≃ c_1(t) v_s(r,t) is introduced without derivation or a clear statement of its validity; it is a modeling assumption for the damped-PVM regime rather than a consequence of the duality.

Circularity Check

4 steps flagged · score 7.0 of 10

Most of Table III is imposed by definitions: the Gauss and Faraday analogues are identities, and the only dynamical equation (the Ampere analogue) does not follow from the preceding equations because the polarization time derivative and an equation for vP are assumed.

  1. self definitional [Section IV, Eqs. (35)-(39)]
    "let us define the vortex charge density ρv (r, t) such that ∫_A d^2r ρv (r, t) := Σ_{j=1}^{N_v(A;t)} q_j (t) . ... D_sf (r, t) := M/(2πℏ) vs (r, t) × e⊥, P_sf (r, t) := D_sf (r, t) − ϵ_sf E_sf (r, t) ... whence it follows that ∇ ·D_sf (r, t) = ρv (r, t) . (39)"

    With D_sf defined as M/(2πℏ) vs × e⊥, the equation ∇·D_sf = ρv is just the statement ρv = (M/2πℏ) e⊥·(∇×vs), i.e., the vortex charge density is identified with the vorticity of the superfluid velocity. The integral definition (35) does not fix ρv pointwise; the pointwise Gauss law is effectively the definition of ρv in terms of the same velocity field used to build D_sf. No equation of motion enters, so the Gauss-law analogue holds by construction rather than by derivation.

  2. other [Section IV, Eqs. (43)-(46)]
    "From Eqs. (22), (36), (38), and (41), we find ∂D_sf (r, t)/∂t = M/(2πℏ) ∂v_P (r, t)/∂t × e⊥ + ∂P_sf (r, t)/∂t = −J_sf (r, t) + ∇ ×(− U_sf (r, t)/(2πℏ) e⊥) . (43)"

    This is the step that would give the Ampere analogue (46) independent dynamical content, but it does not follow by substitution from the quoted equations. Using Eq. (22) in D_sf = M/(2πℏ) vs × e⊥ gives ∂D_sf/∂t = (M/2πℏ)(fK+Fsf−∇Usf) × e⊥, while the right-hand side of Eq. (43) using Eq. (41) is (1/2πℏ)[−e⊥×(fK+Fsf)+e⊥×∇Usf] + ∂Psf/∂t. Equality would require ∂Psf/∂t to cancel and an Euler equation for the pseudo-velocity vP, which is defined only through its curl in Eq. (37). Neither is established for inhomogeneous, time-dependent condensates; the claimed cancellation is the point-vortex-limit assumption in disguise. Thus Eq. (46) is not derived, and the advertised beyond-PVM duality is not supported by the derivation.

2 more flagged steps
  1. self definitional [Section IV, Eqs. (48)-(50)]
    "By defining the effective free magnetic current density Jm,sf (r, t) as [Eq. (49)] ... Eq. (48) can be expressed as ∇ ×D_sf (r, t) = − 1/c_sf^2 (Jm,sf (r, t) + ∂H_sf (r, t)/∂t) . (50)"

    Equation (48) is only an identity obtained from the definitions of Dsf and Psf. The magnetic current Jm,sf is then introduced in Eq. (49) precisely so that, when combined with ∂Hsf/∂t, it cancels the c_sf^2 prefactor and returns Eq. (48). The Faraday analogue therefore contains no dynamical information; it is true by construction. The magnetic current is a bookkeeping term chosen to make the Maxwell form hold, not an independent physical source.

  2. other [Section IV, Eq. (52); used again in Section V for the damped-PVM discussion]
    "Ssf (r, t) = Esf (r, t) × Hsf (r, t) = M vP (r, t)/( (2πℏ)^2 ϵsf ) [Usf (r, t) − ¯Usf (t)], implying that the vortex (free electric charge) moves parallel to vP (r, t), not parallel to the superfluid velocity vs (r, t) in general"

    Since Esf is proportional to vP × e⊥ by Eq. (36) and Hsf is proportional to e⊥ by Eq. (44), the vector identity (vP × e⊥) × e⊥ = vP forces the Poynting vector to point along vP. The direction of Ssf therefore carries no independent information about vortex motion; identifying it with the vortex velocity is an interpretive assertion built into the definitions. Later arguments, including the damped-PVM discussion around Eq. (61), lean on this identification, so a physical prediction is being read out of the dictionary rather than derived from vortex dynamics.

full rationale

Self-citation is not the driving issue: the del Campo/Shinn citations (e.g., Refs. [12,13,97,107]) concern Kibble-Zurek vortex statistics and are not load-bearing for the duality derivation. The score reflects instead that the advertised effective Maxwell equations are largely built from the dictionary. Equation (39) is not independent: with Dsf = M/(2πℏ) vs × e⊥, it restates the vortex charge density as the vorticity of the superfluid velocity. Equation (50) is created by defining Jm,sf to absorb the identity (48), so it is true by construction. Equation (47) is trivial because Hsf is built from a scalar potential times a fixed direction e⊥. The only equation that could give the duality dynamical content, Eq. (46), depends on Eq. (43), which does not follow from Eqs. (22), (36), (38), and (41): direct substitution leaves the time derivative of the effective polarization Psf (the beyond-PVM correction) and requires an unproved Euler equation for vP, a field fixed only by its curl in Eq. (37). The Poynting-vector statement that vortices move along vP is likewise read off from the definitions of Esf and Hsf. Because the central claim is a restructuring of definitions rather than a derived prediction, the circularity score is 7.

Assumptions & free parameters 4 free parameters · 6 assumptions · 2 invented entities

The central construction rests on the GPE and generalized momentum equations, vortex quantization, and a series of definitions for effective fields. No fitted experimental data is used, but several constants and free functions (eps_sf, c_sf, M_sf, c1) enter the duality and are not determined by the underlying physics. The invented entities are mathematical dual variables rather than new physical objects.

free parameters (4)
  • epsilon_sf (effective vacuum permittivity)
    Introduced as 'some constant' in Eqs. (36) and (38); no equation determines it. Affects Esf, Psf, and Bsf, and hence the effective force on vortices.
  • c_sf (effective speed of light) = cs = sqrt(g n_max / M)
    Set to the maximum sound speed by invoking the Landau criterion (Sec. IV), not derived from the mapping. Controls the retarded-potential corrections in Sec. VIII A.
  • M_sf(r,t) (effective magnetization)
    Free function introduced in Eq. (59) to define Bsf. The force in Eq. (60) depends on it, and the damped-PVM is recovered only with a suitable choice.
  • c1(t) (polarization proportionality)
    Introduced in Sec. V when approximating Psf as c1(t) vs; used to express vP and arrive at the damped-PVM.
assumptions (6)
  • domain assumption The system is a quasi-2D scalar Bose gas in the s-wave scattering limit with the Hamiltonian of Eq. (1).
    This restricts the validity of the derivation to dilute scalar BECs with contact interactions.
  • domain assumption The mean-field order parameter psi = <hat psi> obeys the GPE and the continuity and momentum equations (16)-(17).
    Used throughout Sec. II and Sec. IV as the starting point for the duality.
  • domain assumption Vortex quantization: circulation around a vortex is 2 pi hbar / M q_j with integer q_j, and the density is zero at vortex cores.
    Stated in Sec. III, Eq. (29); underlies the delta-function vorticity and the definition of the vortex charge density.
  • domain assumption The generalized equations (20)-(22) with model-dependent G and F describe dissipation and rotation.
    Invoked in Sec. II B; the specific forms of G and F are not needed for the formal Maxwell construction, but their existence as the correct generalization is assumed.
  • ad hoc to paper Distributional manipulation of equations at n=0 vortex cores, including division by n^2, is valid.
    Needed to go from Eq. (22) to Eq. (43) and to define point-like vortex charges; not rigorously justified.
  • domain assumption For the GPE in a nonrotating system, div vs = 0 (cited to Ref. [34]).
    Used in Sec. VIII to write fK as a gradient plus curl; may fail near vortex cores.
invented entities (2)
  • vP (pseudo-superfluid velocity)
    purpose: Used to define the effective electric field Esf and later interpreted as the vortex velocity.
    Defined only by its curl in Eq. (37); no independent equation fixes its irrotational part, and the identification with vortex velocity is asserted.
  • Effective electromagnetic fields and currents (Dsf, Esf, Hsf, Bsf, Jsf, Jm,sf, potentials)
    purpose: Mathematical dictionary between fluid and electromagnetic variables; no new physical fields.
    All are constructed from vs, n, V, fK, and Fsf; there is no experimental handle outside the BEC system that would confirm their reality.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Electrodynamics of Vortices in Quasi-2D Scalar Bose-Einstein Condensates." pith.science (2026). https://pith.science/paper/2WH3HHCH

@misc{pith2026241114302,
  author       = {Pith},
  title        = {Pith review of: Electrodynamics of Vortices in Quasi-2D Scalar Bose-Einstein Condensates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2WH3HHCH}},
  note         = {Machine review of arXiv:2411.14302}
}
read the original abstract

In two spatial dimensions, vortex-vortex interactions approximately vary with the logarithm of the inter-vortex distance, making it possible to describe an ensemble of vortices as a Coulomb gas. We introduce a duality between vortices in a quasi-two-dimensional (quasi-2D) scalar Bose-Einstein condensates (BEC) and effective Maxwell's electrodynamics. Specifically, we address the general scenario of inhomogeneous, time-dependent BEC number density with dissipation or rotation. Starting from the Gross-Pitaevskii equation (GPE), which describes the mean-field dynamics of a quasi-2D scalar BEC without dissipation, we show how to map vortices in a quasi-2D scalar BEC to 2D electrodynamics beyond the point-vortex approximation, even when dissipation is present or in a rotating system. The physical meaning of this duality is discussed.

Figures

Figures reproduced from arXiv: 2411.14302 by the authors.

Figure 1
Figure 1. FIG. 1. Duality between the vortices in the quasi-2D scalar BEC and the electrodynamics in the matter. The derivations are [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

118 extracted references · 69 canonical work pages

  1. [1]

    effective free electric charge,

    Example: rotating quasi-2D scalar BEC without dissipation Motivated by the experiment with two concentric counter-rotating superfluids [70], we will consider a rotating quasi-2D scalar BEC with angular velocity Ω⊥ (r, t) = Ω⊥ (r, t) e⊥ thatdependsonpositionortime. In the rotating frame, the GPE in Eq. (6) becomes [57] iℏ ∂ψ (r, t) ∂t = − ℏ2 2M ∇2 + V (r, ...

  2. [2]

    T. W. B. Kibble, Some implications of a cosmological phase transition, Physics Reports67, 183 (1980)

    1980

  3. [3]

    (56) under the specific system in the regionA one studies

    The correction due to the nonzeroJsf (r, t) is of or- der O |r − rα1 (t)|2 / (csf t)2 relative to v(0) s;1 (r, t), but further evaluation needs numerical calculations to solve Eq. (56) under the specific system in the regionA one studies. One may consider it as solving the effective Liénard–Wiechert potentials in (2+1) dimensional space- time since vortic...

    work page arXiv

  4. [4]

    T. W. B. Kibble, Topology of cosmic domains and strings, Journal of Physics A: Mathematical and Gen- eral 9, 1387 (1976)

    1976

  5. [5]

    del Campo and W

    A. del Campo and W. H. Zurek, Universality of phase transition dynamics: Topological defects from symme- try breaking, International Journal of Modern Physics A 29, 1430018 (2014)

    2014

  6. [6]

    W. H. Zurek, Cosmological experiments in superfluid helium?, Nature 317, 505 (1985)

    1985

  7. [7]

    W. H. Zurek, Cosmic strings in laboratory superfluids and the topological remnants of other phase transitions, Acta physica polonica. B24, 1301 (1993)

    1993

  8. [8]

    Kawaguchi and M

    Y. Kawaguchi and M. Ueda, Spinor bose–einstein con- densates, Physics Reports520, 253 (2012)

    2012

Show all 118 references
  1. [9]

    N. D. Mermin, The topological theory of defects in or- dered media, Rev. Mod. Phys.51, 591 (1979)

    1979

  2. [10]

    Manton and P

    N. Manton and P. Sutcliffe,Topological Solitons, Cam- bridge Monographs on Mathematical Physics (Cam- bridge University Press, Cambridge, 2004)

    2004

  3. [11]

    C. J. Pethick and H. Smith,Bose-Einstein Condensa- tion in Dilute Gases, 2nd ed. (Cambridge University Press, Cambridge, 2008)

    2008

  4. [12]

    D. R. Nelson,Defects and Geometry in Condensed Mat- ter Physics (Cambridge University Press, Cambridge, 2002)

    2002

  5. [13]

    A. L. Fetter and A. A. Svidzinsky, Vortices in a trapped dilute bose-einstein condensate, Journal of Physics: Condensed Matter 13, R135 (2001)

    2001

  6. [14]

    C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, and B. P. Anderson, Spontaneous vortices in the formation of Bose-Einstein condensates, Nature 455, 948 (2008)

    2008

  7. [15]

    Zeng, C.-Y

    H.-B. Zeng, C.-Y. Xia, and A. del Campo, Univer- sal breakdown of kibble-zurek scaling in fast quenches across a phase transition, Phys. Rev. Lett.130, 060402 (2023)

    2023

  8. [16]

    Thudiyangal and A

    M. Thudiyangal and A. del Campo, Universal vortex statistics and stochastic geometry of bose-einstein con- densation, Phys. Rev. Res.6, 033152 (2024)

    2024

  9. [17]

    J. Goo, Y. Lee, Y. Lim, D. Bae, T. Rabga, and Y. Shin, Universalearlycoarseningofquenchedbosegases,Phys. Rev. Lett. 128, 135701 (2022). 15

    2022

  10. [18]

    beyond the GPE

    or the superfluid cloud, pumping angular momen- tum in the system [19, 20]. Vortices in degenerate ul- tracold gases can also be produced by phase imprinting [21–23], by merging independent BEC [24], by stirring laser beams [25–29], or by making superfluid flow pass an obstacl...

    2025 arXiv

  11. [19]

    Chomaz, L

    L. Chomaz, L. Corman, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Beugnon, and J. Dal- ibard, Emergence of coherence via transverse condensa- tion in a uniform quasi-two-dimensional bose gas, Na- ture Communications 6, 6162 (2015)

    2015

  12. [20]

    J. Goo, Y. Lim, and Y. Shin, Defect saturation in a rapidlyquenchedbosegas,Phys.Rev.Lett. 127,115701 (2021)

    2021

  13. [21]

    P. C. Haljan, I. Coddington, P. Engels, and E. A. Cor- nell, Driving bose-einstein-condensate vorticity with a rotating normal cloud, Phys. Rev. Lett. 87, 210403 (2001)

    2001

  14. [22]

    J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ket- terle, Observation of vortex lattices in bose-einstein con- densates, Science 292, 476 (2001)

    2001

  15. [23]

    A. L. Fetter, Rotating trapped bose-einstein conden- sates, Rev. Mod. Phys.81, 647 (2009)

    2009

  16. [24]

    M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, Vortices in a bose-einstein condensate, Phys. Rev. Lett. 83, 2498 (1999)

    1999

  17. [25]

    A. E. Leanhardt, A. Görlitz, A. P. Chikkatur, D. Kielpinski, Y. Shin, D. E. Pritchard, and W. Ket- terle, Imprinting vortices in a bose-einstein condensate using topological phases, Phys. Rev. Lett. 89, 190403 (2002)

    2002

  18. [26]

    J. F. S. Brachmann, W. S. Bakr, J. Gillen, A. Peng, and M. Greiner, Inducing vortices in a bose-einstein conden- sate using holographically produced light beams, Opt. Express 19, 12984 (2011)

    2011

  19. [27]

    D. R. Scherer, C. N. Weiler, T. W. Neely, and B. P. Anderson, Vortex formation by merging of multiple trapped bose-einstein condensates, Phys. Rev. Lett.98, 110402 (2007)

    2007

  20. [28]

    K. W. Madison, F. Chevy, W. Wohlleben, and J. Dal- ibard, Vortex formation in a stirred bose-einstein con- densate, Phys. Rev. Lett.84, 806 (2000)

    2000

  21. [29]

    Raman, J

    C. Raman, J. R. Abo-Shaeer, J. M. Vogels, K. Xu, and W. Ketterle, Vortex nucleation in a stirred bose-einstein condensate, Phys. Rev. Lett.87, 210402 (2001)

    2001

  22. [30]

    Damski, K

    B. Damski, K. Sacha, and J. Zakrzewski, Stirring a bose–einstein condensate, Journal of Physics B: Atomic, Molecular and Optical Physics35, 4051 (2002)

    2002

  23. [31]

    E. A. L. Henn, J. A. Seman, G. Roati, K. M. F. Mag- alhães, and V. S. Bagnato, Emergence of turbulence in an oscillating bose-einstein condensate, Phys. Rev. Lett. 103, 045301 (2009)

    2009

  24. [32]

    Gauthier, M

    G. Gauthier, M. T. Reeves, X. Yu, A. S. Bradley, M. A. Baker, T. A. Bell, H. Rubinsztein-Dunlop, M. J. Davis, and T. W. Neely, Giant vortex clusters in a two- dimensional quantum fluid, Science364, 1264 (2019)

    2019

  25. [33]

    T. W. Neely, E. C. Samson, A. S. Bradley, M. J. Davis, and B. P. Anderson, Observation of vortex dipoles in an oblate bose-einstein condensate, Phys. Rev. Lett.104, 160401 (2010)

    2010

  26. [34]

    T. W. Neely, G. Gauthier, C. Glasspool, M. J. Davis, and M. T. Reeves, Melting of a vortex matter wigner crystal (2024), arXiv:2402.09920 [cond-mat.quant-gas]

    2024 arXiv

  27. [35]

    B. I. Halperin,Superfluidity, melting, and liquid-crystal phases in two dimensions,inProceedingsofKyotoSum- merInstitute1979-PhysicsofLowDimensionalSystems (Publication Office, Progress of Theoretical Physics, Kyoto University, 1979) p. 53

    1979

  28. [36]

    Ambegaokar, B

    V. Ambegaokar, B. I. Halperin, D. R. Nelson, and E. D. Siggia, Dynamics of superfluid films, Phys. Rev. B21, 1806 (1980)

    1980

  29. [37]

    Kleinert,Gauge Fields in Condensed Matter(World Scientific, Singapore, 1989)

    H. Kleinert,Gauge Fields in Condensed Matter(World Scientific, Singapore, 1989)

    1989

  30. [38]

    Kleinert, Multivalued Fields (World Scientific, Sin- gapore, 2008)

    H. Kleinert, Multivalued Fields (World Scientific, Sin- gapore, 2008)

    2008

  31. [39]

    J. C. Neu, Vortices in complex scalar fields, Physica D: Nonlinear Phenomena 43, 385 (1990)

    1990

  32. [40]

    J. C. Neu, Vortex dynamics of the nonlinear wave equa- tion, Physica D: Nonlinear Phenomena43, 407 (1990)

    1990

  33. [41]

    U. R. Fischer, Motion of quantized vortices as elemen- tary objects, Annals of Physics278, 62 (1999)

    1999

  34. [42]

    Simula, Gravitational vortex mass in a superfluid, Phys

    T. Simula, Gravitational vortex mass in a superfluid, Phys. Rev. A101, 063616 (2020)

    2020

  35. [43]

    E. G. Johansen, A correspondence between maxwell–einstein theory and superfluidity (2024), arXiv:2405.18090 [cond-mat.quant-gas]

    2024 arXiv

  36. [44]

    V. L. Ginzburg and L. P. Pitaevskii, On the theory of superfluidity, Sov. Phys. JETP7, 858 (1958)

    1958

  37. [45]

    P. J. Torres, R. Carretero-González, S. Middelkamp, P. Schmelcher, D. J. Frantzeskakis, and P. Kevrekidis, Vortex interaction dynamics in trapped bose-einstein condensates, Communications on Pure and Applied Analysis 10, 1589 (2011)

    2011

  38. [46]

    Richaud, V

    A. Richaud, V. Penna, and A. L. Fetter, Dynamics of massive point vortices in a binary mixture of bose- einstein condensates, Phys. Rev. A103, 023311 (2021)

    2021

  39. [47]

    Richaud, G

    A. Richaud, G. Lamporesi, M. Capone, and A. Recati, Mass-driven vortex collisions in flat superfluids, Phys. Rev. A 107, 053317 (2023)

    2023

  40. [48]

    T. C. Corso, G. Kemlin, C. Melcher, and B. Stamm, Nu- merical simulation of the gross-pitaevskii equation via vortex tracking (2024), arXiv:2404.02133 [math.NA]

    2024

  41. [49]

    Castin and R

    Y. Castin and R. Dum, Low-temperature bose-einstein condensates in time-dependent traps: Beyond theu(1) symmetry-breaking approach, Phys. Rev. A 57, 3008 (1998)

    1998

  42. [50]

    Pitaevskii, Phenomenological theory of superfluidity near the λ point, Sov

    L. Pitaevskii, Phenomenological theory of superfluidity near the λ point, Sov. Phys. JETP8, 282 (1959)

    1959

  43. [51]

    C. W. Gardiner, P. Zoller, R. J. Ballagh, and M. J. Davis, Kinetics of bose-einstein condensation in a trap, Phys. Rev. Lett.79, 1793 (1997)

    1997

  44. [52]

    S. Choi, S. A. Morgan, and K. Burnett, Phenomenolog- ical damping in trapped atomic bose-einstein conden- sates, Phys. Rev. A57, 4057 (1998)

    1998

  45. [53]

    Kasamatsu, M

    K. Kasamatsu, M. Tsubota, and M. Ueda, Nonlinear dynamics of vortex lattice formation in a rotating bose- einstein condensate, Phys. Rev. A67, 033610 (2003)

    2003

  46. [54]

    P. B. Blakie, A. S. Bradley, M. J. Davis, R. J. Ballagh, and C. W. Gardiner, Dynamics and statistical mechan- ics of ultra-cold bose gases using c-field techniques, Ad- vances in Physics57, 363 (2008)

    2008

  47. [55]

    Damski and W

    B. Damski and W. H. Zurek, Soliton creation dur- ing a bose-einstein condensation, Phys. Rev. Lett.104, 160404 (2010)

    2010

  48. [56]

    A. S. Bradley, S. J. Rooney, and R. G. McDonald, Low- dimensional stochastic projected gross-pitaevskii equa- tion, Phys. Rev. A92, 033631 (2015)

    2015

  49. [57]

    I.-K. Liu, J. Dziarmaga, S.-C. Gou, F. Dalfovo, and N. P. Proukakis, Kibble-zurek dynamics in a trapped ultracold bose gas, Phys. Rev. Res.2, 033183 (2020)

    2020

  50. [58]

    Rica and E

    S. Rica and E. Tirapegui, Interaction of defects in two- dimensional systems, Phys. Rev. Lett.64, 878 (1990)

    1990

  51. [59]

    Mehdi, J

    Z. Mehdi, J. J. Hope, S. S. Szigeti, and A. S. Bradley, Mutual friction and diffusion of two-dimensional quan- tum vortices, Phys. Rev. Res.5, 013184 (2023)

    2023

  52. [60]

    Pitaevskii and S

    L. Pitaevskii and S. Stringari,Bose-Einstein Conden- sation, International Series of Monographs on Physics (Clarendon Press, Oxford, 2003)

    2003

  53. [61]

    E. P. Gross, Structure of a quantized vortex in boson systems, Il Nuovo Cimento20, 454 (1961)

    1961

  54. [62]

    L. P. Pitaevskii, Vortex lines in an imperfect bose gas, 16 Sov. Phys. JETP13, 451 (1961)

    1961

  55. [63]

    Bohm and B

    D. Bohm and B. Hiley,The undivided universe: an on- tological interpretation of quantum theory, Physics, phi- losophy (Routledge, Oxford, 1995)

    1995

  56. [64]

    Trahan and R

    C. Trahan and R. Wyatt, Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics, Interdisciplinary Applied Mathematics (Springer New York, 2005)

    2005

  57. [65]

    Madelung, Quantentheorie in hydrodynamischer form, Zeitschrift für Physik40, 322 (1927)

    E. Madelung, Quantentheorie in hydrodynamischer form, Zeitschrift für Physik40, 322 (1927)

    1927

  58. [66]

    Bohm, A suggested interpretation of the quantum theory in terms of "hidden" variables

    D. Bohm, A suggested interpretation of the quantum theory in terms of "hidden" variables. i, Phys. Rev.85, 166 (1952)

    1952

  59. [67]

    Takabayasi, On the formulation of quantum mechan- ics associated with classical pictures*, Progress of The- oretical Physics 8, 143 (1952)

    T. Takabayasi, On the formulation of quantum mechan- ics associated with classical pictures*, Progress of The- oretical Physics 8, 143 (1952)

    1952

  60. [68]

    B. I. Halperin, Statistical mechanics of topological de- fects, in Physics of Defects, Les Houches 1980 Session XXXV (North-Holland, Amsterdam, 1981) p. 813

    1980

  61. [69]

    R. P. Feynman, Application of quantum mechanics to liquid helium, Prog. Low Temp. Phys.1, 17 (1955)

    1955

  62. [70]

    P. W. Anderson, Considerations on the flow of super- fluid helium, Rev. Mod. Phys.38, 298 (1966)

    1966

  63. [71]

    H. Kleinert, Theory of fluctuating nonholonomic fields and applications: Statistical mechanics of vortices and defects and new physical laws in spaces with curvature and torsion, inFormation and Interactions of Topologi- cal Defects: Proceedings of a NATO Advanced Study In- st...

    1994

  64. [72]

    G. F. Mazenko, Vortex velocities in theO(n) symmet- ric time-dependent ginzburg-landau model, Phys. Rev. Lett. 78, 401 (1997)

    1997

  65. [73]

    D.Hernández-Rajkov, N.Grani, F.Scazza, G.DelPace, W. J. Kwon, M. Inguscio, K. Xhani, C. Fort, M. Mod- ugno, F. Marino, and G. Roati, Connecting shear flow and vortex array instabilities in annular atomic super- fluids, Nature Physics20, 939 (2024)

    2024

  66. [74]

    J. J. García-Ripoll, G. Molina-Terriza, V. M. Pérez- García, and L. Torner, Structural instability of vor- tices in bose-einstein condensates, Phys. Rev. Lett.87, 140403 (2001)

    2001

  67. [75]

    G.Biroli, L.F.Cugliandolo,andA.Sicilia,Kibble-zurek mechanismandinfinitelyslowannealingthroughcritical points, Phys. Rev. E81, 050101 (2010)

    2010

  68. [76]

    P. M. Chesler, A. M. García-García, and H. Liu, Defect formation beyond kibble-zurek mechanism and hologra- phy, Phys. Rev. X5, 021015 (2015)

    2015

  69. [77]

    I.-K. Liu, S. Donadello, G. Lamporesi, G. Ferrari, S.- C. Gou, F. Dalfovo, and N. P. Proukakis, Dynamical equilibration across a quenched phase transition in a trapped quantum gas, Communications Physics 1, 24 (2018)

    2018

  70. [78]

    M. V. Berry and P. Shukla, Quantum curl forces, Jour- nal of Physics A: Mathematical and Theoretical 56, 485206 (2023)

    2023

  71. [79]

    Rønning and L

    J. Rønning and L. Angheluta, Precursory patterns to vortex nucleation in stirred bose-einstein condensates, Phys. Rev. Res.5, 023108 (2023)

    2023

  72. [80]

    Skogvoll, J

    V. Skogvoll, J. Rønning, M. Salvalaglio, and L. Anghe- luta, A unified field theory of topological defects and non-linear local excitations, npj Computational Materi- als 9, 122 (2023)

    2023

  73. [81]

    L. D. Landau, The theory of superfuidity of helium II, J. Phys. (USSR)5, 71 (1941)

    1941

  74. [82]

    Watanabe, Integral Transform Techniques for Green’s Function, Lecture Notes in Applied and Com- putational Mechanics (Springer International Publish- ing Switzerland, Cham, 2015)

    K. Watanabe, Integral Transform Techniques for Green’s Function, Lecture Notes in Applied and Com- putational Mechanics (Springer International Publish- ing Switzerland, Cham, 2015)

    2015

  75. [83]

    Boito, L

    D. Boito, L. N. S. de Andrade, G. de Sousa, R. Gama, and C. Y. M. London, On maxwell’s electrodynamics in two spatial dimensions, Revista Brasileira de Ensino de Física 42, e20190323 (2020)

    2020

  76. [84]

    Gürses, Metin and Sarıoğlu, Özgür, Liénard–Wiechert potentials in even dimensions, Journal of Mathematical Physics 44, 4672 (2003)

    2003

  77. [85]

    Reynolds,Papers on Mechanical and Physical Sub- jects

    O. Reynolds,Papers on Mechanical and Physical Sub- jects. Vol. 3, The Sub-Mechanics of the Universe (Cam- bridge University Press, Cambridge, 1903)

    1903

  78. [86]

    Kundu, I

    P. Kundu, I. Cohen, and D. Dowling,Fluid Mechanics, 5th ed. (Academic Press, Cambridge, Massachusetts, 2012)

    2012

  79. [87]

    Kozik and B

    E. Kozik and B. Svistunov, Vortex-phonon interaction, Phys. Rev. B72, 172505 (2005)

    2005

  80. [88]

    W. J. Kwon, G. Del Pace, K. Xhani, L. Galantucci, A. Muzi Falconi, M. Inguscio, F. Scazza, and G. Roati, Sound emission and annihilations in a programmable quantum vortex collider, Nature600, 64 (2021)

    2021

  81. [89]

    M. Lazar, On the non-uniform motion of dislocations: the retarded elastic fields, the retarded dislocation ten- sor potentials and the liénard–wiechert tensor poten- tials, Philosophical Magazine93, 749 (2013)

    2013

  82. [90]

    Tsaloukidis and P

    L. Tsaloukidis and P. Surówka, Elastic liénard-wiechert potentials of dynamical dislocations from tensor gauge theory in 2 + 1 dimensions, Phys. Rev. B109, 104118 (2024)

    2024

  83. [91]

    O. D. Jefimenko,Electricity and Magnetism: An Intro- duction to the Theory of Electric and Magnetic Fields (New York: Appleton-Century-Crofts, 1966)

    1966

  84. [92]

    D. J. Griffiths,Introduction to Electrodynamics, 4th ed. (Cambridge University Press, Cambridge, 2017)

    2017

  85. [93]

    sine-gordon

    J. Fröhlich, Quantized "sine-gordon" equation with a nonvanishing mass term in two space-time dimensions, Phys. Rev. Lett.34, 833 (1975)

    1975

  86. [94]

    Fröhlich, Quantum sine-gordon equation and quan- tumsolitonsintwospace-timedimensions,in Renormal- ization Theory, edited by G

    J. Fröhlich, Quantum sine-gordon equation and quan- tumsolitonsintwospace-timedimensions,in Renormal- ization Theory, edited by G. Velo and A. S. Wightman (Springer Netherlands, Dordrecht, 1976) pp. 371–414

    1976

  87. [95]

    Coleman, Quantum sine-gordon equation as the mas- sive thirring model, Phys

    S. Coleman, Quantum sine-gordon equation as the mas- sive thirring model, Phys. Rev. D11, 2088 (1975)

    1975

  88. [96]

    Samuel, Grand partition function in field theory with applications to sine-gordon field theory, Phys

    S. Samuel, Grand partition function in field theory with applications to sine-gordon field theory, Phys. Rev. D 18, 1916 (1978)

    1978

  89. [97]

    V. L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems possess- ing a continuous symmetry group. ii. quantum systems, Sov. Phys. JETP34, 610 (1972)

    1972

  90. [98]

    J. M. Kosterlitz and D. J. Thouless, Ordering, metasta- bility and phase transitions in two-dimensional systems, Journal of Physics C: Solid State Physics6, 1181 (1973)

    1973

  91. [99]

    Šamaj and I

    L. Šamaj and I. Travěnec, Thermodynamic properties of the two-dimensional two-component plasma, Journal of Statistical Physics101, 713 (2000)

    2000

  92. [100]

    del Campo, F

    A. del Campo, F. J. Gómez-Ruiz, and H.-Q. Zhang, Lo- cality of spontaneous symmetry breaking and universal spacing distribution of topological defects formed across 17 a phase transition, Phys. Rev. B106, L140101 (2022)

    2022

  93. [101]

    G.Akemann, A.Mielke,andP.Päßler,Spacingdistribu- tion in the two-dimensional coulomb gas: Surmise and symmetry classes of non-hermitian random matrices at noninteger β, Phys. Rev. E106, 014146 (2022)

    2022

  94. [102]

    Massaro and A

    M. Massaro and A. del Campo, Spatial form factor for point patterns: Homogeneous poisson point process and coulomb gas (2024), arXiv:2410.04816 [cond-mat.stat- mech]

    2024 arXiv

  95. [103]

    M. C. Tsatsos, P. E. Tavares, A. Cidrim, A. R. Fritsch, M. A. Caracanhas, F. E. A. dos Santos, C. F. Barenghi, and V. S. Bagnato, Quantum turbulence in trapped atomic bose–einstein condensates, Physics Reports622, 1 (2016)

    2016

  96. [104]

    M. T. Reeves, K. Goddard-Lee, G. Gauthier, O. R. Stockdale, H. Salman, T. Edmonds, X. Yu, A. S. Bradley, M. Baker, H. Rubinsztein-Dunlop, M. J. Davis, and T. W. Neely, Turbulent relaxation to equilibrium in a two-dimensional quantum vortex gas, Phys. Rev. X 12, 011031 (2022)

    2022

  97. [105]

    del Campo, Frictionless quantum quenches in ultra- cold gases: A quantum-dynamical microscope, Phys

    A. del Campo, Frictionless quantum quenches in ultra- cold gases: A quantum-dynamical microscope, Phys. Rev. A 84, 031606 (2011)

    2011

  98. [106]

    del Campo, Shortcuts to adiabaticity by counterdia- batic driving, Phys

    A. del Campo, Shortcuts to adiabaticity by counterdia- batic driving, Phys. Rev. Lett.111, 100502 (2013)

    2013

  99. [107]

    D. J. Papoular and S. Stringari, Shortcut to adiabaticity forananisotropicgascontainingquantumdefects,Phys. Rev. Lett. 115, 025302 (2015)

    2015

  100. [108]

    Navon, A

    N. Navon, A. L. Gaunt, R. P. Smith, and Z. Hadzibabic, Critical dynamics of spontaneous symmetry breaking in a homogeneous bose gas, Science347, 167 (2015)

    2015

  101. [109]

    M. Kim, J. Kwon, T. Rabga, and Y. Shin, Vortex detec- tion in atomic Bose-Einstein condensates using neural networks trained on synthetic images, Machine Learn- ing: Science and Technology4, 045017 (2023)

    2023

  102. [110]

    del Campo, A

    A. del Campo, A. Retzker, and M. B. Plenio, The inho- mogeneous Kibble-Zurek mechanism: vortex nucleation during Bose-Einstein condensation, New J. Phys. 13, 083022 (2011)

    2011

  103. [111]

    F. J. Gómez-Ruiz, J. J. Mayo, and A. del Campo, Full counting statistics of topological defects after crossing a phase transition, Phys. Rev. Lett.124, 240602 (2020)

    2020

  104. [112]

    del Campo, F

    A. del Campo, F. J. Gómez-Ruiz, Z.-H. Li, C.-Y. Xia, H.-B.Zeng,andH.-Q.Zhang,Universalstatisticsofvor- tices in a newborn holographic superconductor: beyond the kibble-zurek mechanism, Journal of High Energy Physics 2021, 61 (2021)

    2021

  105. [113]

    Xia, H.-B

    C.-Y. Xia, H.-B. Zeng, A. Grabarits, and A. del Campo, Kibble-zurek mechanism and beyond: Lessons from a holographic superfluid disk (2024), arXiv:2406.09433 [cond-mat.stat-mech]

    2024 arXiv

  106. [114]

    Lahaye, C

    T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, The physics of dipolar bosonic quantum gases, Reports on Progress in Physics72, 126401 (2009)

    2009

  107. [115]

    Carusotto and C

    I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013)

    2013

  108. [116]

    Fujiyama and M

    S. Fujiyama and M. Tsubota, Drag force on an oscil- lating object in quantum turbulence, Phys. Rev. B79, 094513 (2009)

    2009

  109. [117]

    Adachi, S

    H. Adachi, S. Fujiyama, and M. Tsubota, Steady-state counterflow quantum turbulence: Simulation of vortex filaments using the full biot-savart law, Phys. Rev. B 81, 104511 (2010)

    2010

  110. [118]

    Serafini, M

    S. Serafini, M. Barbiero, M. Debortoli, S. Donadello, F. Larcher, F. Dalfovo, G. Lamporesi, and G. Ferrari, Dynamics and interaction of vortex lines in an elongated bose-einstein condensate, Phys. Rev. Lett.115, 170402 (2015)

    2015

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.