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REVIEW 4 major objections 5 minor 46 references

Superfluidity fraction of few bosons in an annular geometry in the presence of a rotating weak link

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A rotating barrier suppresses superfluidity but leaves condensation intact

desk verdict Useful MCTDHB study of few-boson ring superfluidity, but the central numerical claim rests on convergence details the paper never reports, and the abstract overstates the condensate-fraction independence. read the letter →

arxiv 1908.02351 v1 pith:26ZWDPMT submitted 2019-08-06 cond-mat.quant-gas quant-ph

Alex V. Andriati , Arnaldo Gammal This is my paper · ORCID
classification cond-mat.quant-gasquant-ph
keywords superfluidityfractionfewbosonsringgeometryrotatingweaklinkMCTDHBBose-Einsteincondensationone-bodycorrelationfunctionpersistentcurrent
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 asks whether a moving potential barrier (a weak link) can degrade superfluid flow in a ring of just a few interacting bosons, and whether that degradation is tied to the loss of Bose-Einstein condensation. Using a beyond-mean-field variational method, the authors compute ground states for up to 11 particles and extract the superfluid fraction from the energy's response to rotation. They find that raising the barrier height steadily drives the superfluid fraction from 1 toward 0, while the condensation fraction, the largest natural-orbital occupation, depends almost exclusively on interaction strength. The conclusion is that, in this few-body system, the suppression of dissipationless flow and the loss of condensation are independent effects. This matters because it separates two concepts often conflated in cold-atom rings and yields experimentally relevant predictions for weak-link atomtronic devices.

What carries the argument

The load-bearing machinery is the MCTDHB ansatz, in which the many-body wavefunction is a superposition of all Fock configurations distributing $N$ bosons over $M$ self-consistently optimized single-particle orbitals, with the Gross-Pitaevskii equation as the single-orbital special case. From the resulting ground state, the authors construct the reduced one-body density matrix, decompose the particle current into natural-orbital contributions, and extract the superfluid fraction from the derivative of the ground-state energy with respect to rotation, equivalently from the ratio of the moment of inertia to the rigid-body value. The normalized first-order correlation function $g^{(1)}(x,x')$, interpreted as the tunneling amplitude between two points weighted by the local densities, is the diagnostic that connects barrier height to the loss of superflow.

What would settle it

Repeat the same parameter sets with an exact or much larger-basis few-boson calculation, increasing the number of orbitals until all observables stop changing, and check whether the superfluid fraction at fixed barrier height shifts by more than the paper's stated accuracy; alternatively, measure the condensation fraction while sweeping barrier height at fixed interaction strength in a cold-atom ring and look for a change larger than the few-percent variation reported in the table.

Watch

Extended reading notes

Core claim

The central claim is that the superfluid fraction $\langle \rho_s\rangle_0$, defined as the zero-rotation limit of $\langle\rho_s\rangle(\Omega) = (2\pi^2 N\Omega)^{-1}\partial E/\partial\Omega$, decreases monotonically as the rotating Gaussian barrier height $\lambda$ is increased, while the condensation fraction, the largest eigenvalue of the reduced one-body density matrix, remains essentially constant across the same range of $\lambda$. The authors show this for $N = 5, 8, 11$ bosons with contact interactions of strength $\gamma$ from $0.1$ to $30$, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). They also show that the ground-state energy is periodic in the dimensionless rotation frequency $\Omega$, that strong barriers drag a finite fraction of particles even at infinitesimal rotation, and that the normalized one-body correlation function $|g^{(1)}(x,x')|^2$ develops an abrupt four-block suppression across the barrier that predicts the flow behavior.

Load-bearing premise

The numerical results assume that the truncated variational basis, the number of single-particle orbitals and Fock configurations in the MCTDHB calculation, is large enough to be converged for every interaction strength and barrier height reported, yet the paper never states the basis size and for the strongest interaction it reports only five particles.

Editorial extensions

If this is right

  • If the central claim is right, a weak-link barrier can tune a few-boson ring continuously from a perfect superfluid to a near-rigid rotor without depleting the condensate.
  • Measuring the ground-state energy versus rotation frequency already determines the superfluid fraction, since the slope at $\Omega=0$ gives $\langle\rho_s\rangle_0$.
  • The correlation-function maps imply that particles are dragged by the barrier whenever the normalized tunneling amplitude across the barrier is suppressed, providing a static, measurable proxy for a dynamical property.
  • At very high barriers the density vanishes at the barrier peak while the angular-momentum distribution broadens only slightly, so loss of superflow is not accompanied by a large momentum change at rest.

Reading between the lines

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

  • If the independence of condensation and superfluid fraction survives at larger particle numbers, it would strengthen the SQUID analogy: the weak link controls dissipationless transport while the condensate, the analogue of the superconducting order parameter, remains intact.
  • A natural extension would be to vary the barrier width and shape at fixed height; the authors' argument suggests the controlling variable is the tunneling amplitude through the barrier, so different shapes with equal tunneling suppression should yield equal superfluid fractions.
  • The same energy-derivative definition could be applied to time-dependent protocols in which the barrier is suddenly raised, predicting metastable current decay rates for a ring prepared in a persistent-flow state.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript studies few bosons (N=5, 8, 11) confined to a ring and subject to a rotating barrier (weak link), using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). The authors derive the mass current from the continuity equation, express the superfluid fraction through the energy derivative with respect to the rotation frequency, and compute it numerically from ground states obtained by imaginary-time propagation. They report that the superfluid fraction at rest decreases from 1 toward 0 as the barrier height increases, while the condensate fraction (largest eigenvalue of the one-body density matrix) is only weakly affected, and they interpret the physics via the one-body correlation function g^(1). The central claim is that barrier-induced suppression of superfluidity is independent of condensation, which would mean a rotating weak link can impede dissipationless flow without destroying the condensate in a few-body system.

Significance. If the numerical results are quantitatively reliable, the paper provides a beyond-mean-field demonstration that in a few-boson ring the superfluid fraction and the condensate fraction respond very differently to a moving barrier, which is directly relevant to persistent-flow and atomtronic experiments. The derivation of the superfluid fraction from the energy derivative is standard and internally consistent, and the authors explicitly check their finite-difference procedure against the momentum formula with a claimed sub-1% deviation. The use of MCTDHB goes beyond the Gross-Pitaevskii level and allows access to correlation functions that are exactly unity in mean-field theory, yielding falsifiable predictions for g^(1). The main weakness is that the variational convergence of the MCTDHB calculations is not documented, and the abstract overstates what Table I actually shows.

major comments (4)
  1. [Section IV, Fig. 5 and Table I] The MCTDHB calculations are not documented with the number of single-particle orbitals M, the spatial grid size, or the imaginary-time step, and no convergence data are shown anywhere. The Conclusion states that the method 'enable us to check convergence ... enlarging the basis', but no such check is reported. This is a load-bearing gap because the high-barrier, strong-interaction corner (λ up to 10^4, γ=30) is precisely where a truncated variational basis and a finite grid are most likely to bias both the superfluid fraction and the largest eigenvalue of the one-body density matrix. Please provide convergence tests with increasing M and grid resolution for representative parameter points, or explicitly restrict the quantitative claims to the converged regime.
  2. [Abstract and Conclusions] The statement that the condensation fraction 'depends exclusively on the interaction strength' is stronger than the data in Table I support. For N=5, γ=30 the maximum/minimum condensation fraction changes from 0.75 to 0.70 as λ varies, and the values also depend on N (e.g., 0.9962 for N=5 versus 0.9936 for N=11 at γ=1). The claim should be softened to state that the condensation fraction depends weakly on the barrier height and predominantly on the interaction strength.
  3. [Section IV, paragraph after Eq. (15)] The approximation ⟨ρ_s⟩0 ≈ ⟨ρ_s⟩(0.01), obtained by a finite difference between Ω=0 and Ω=0.02, is justified only by the assertion of a less than 1% deviation from Eq. (12); no data, table, or plot is provided to support this check. Please show the comparison between Eqs. (13) and (12) for the parameter points used, and ideally display ⟨ρ_s⟩(Ω) in the small-Ω region for several barrier heights so the extrapolation to Ω=0 can be assessed.
  4. [Fig. 5 and Table I] Because results for γ=30 are available only for N=5 (as acknowledged in the Table I caption), the conclusion that 'the number of particles and strength of interactions have a small impact in the form of the curves of ⟨ρ_s⟩0 as a function of λ' is not supported for strong interactions. Either extend the calculations to N=8 and N=11 at γ=30, or restrict the claim to the parameter range actually computed.
minor comments (5)
  1. [Throughout] The manuscript contains numerous typographical errors, including 'tunnable' (Introduction), 'eingenstates' and 'eingenvalue' (Section III), 'in unis of' (Section II), and 'the strenght' (Section IV). A careful proofread is needed.
  2. [Section III and Conclusions] The crossing points of the single-particle parabolas are denoted Ω̃_j = (j + 1/2) in Section III, but in the Conclusions the same points are called Ω_j = (j + 1/2) and described as 'peaks'; the notation should be made consistent.
  3. [Fig. 3] The y-axis of panel (B) is labeled ⟨ρ_s⟩(Ω), while the caption calls it 'current fraction' and the text refers to 'current fraction' in the discussion after Eq. (15). Please align the terminology used in the main text, equations, and figures.
  4. [Eq. (11)] The period τ = 2πR/v is introduced only inside Eq. (11); defining it in the text before the equation would make the expression clearer.
  5. [Section II] The variational equations resulting from the MCTDHB ansatz are cited to Refs. [30,38] but are not written out; stating the coupled equations for C_α and the orbitals would make the numerical implementation more transparent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: superfluid fraction and condensation fraction are computed from independent many-body observables, and no fitted parameter is relabeled as a prediction.

full rationale

The superfluid fraction is obtained from the ground-state energy derivative with respect to rotation frequency via Eq. (15), while the condensation fraction is the largest eigenvalue of the one-body density matrix as reported in Table I. These are distinct, independently defined observables, and neither is fitted to the other. The MCTDHB method is a variational approach cited to prior literature, and the paper states that its own code matches the examples of the published MCTDH-X package, which constitutes independent support rather than a load-bearing self-citation. The decrease of the superfluid fraction with barrier height and the weak dependence of the condensation fraction on barrier height are numerical results of the ground-state computation, not consequences of the definitions. The abstract's claim that the condensation fraction depends 'exclusively' on interaction strength is stronger than Table I, which shows small variations with lambda, but exaggerating a numerical result is a correctness concern, not circularity. The unreported convergence parameters (M, grid size, imaginary-time step) and the admitted code limitation for gamma=30 are validation concerns, not evidence that any result reduces to its own input. No equation in the paper reduces to another by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper fits no data and introduces no new physical entities; its main numerical choices are the barrier width σ=0.1 and the unreported MCTDHB truncation M, both of which are fixed without a reported convergence analysis. The physical parameters γ, λ, N, and Ω are scanned parameters, not fitted constants.

free parameters (2)
  • barrier width σ = 0.1
    Fixed by hand in Eq. (16) for all simulations; the sensitivity of the results to this width is not reported.
  • MCTDHB orbital number M = not reported
    Truncation parameter for the MCTDHB expansion in Eq. (3); never stated in the paper, so the reader cannot assess convergence.
assumptions (4)
  • domain assumption The 1D contact interaction g1D δ(x-x') in Eq. (2) accurately models the interparticle interaction in the ring.
    Standard for tightly transversely confined quasi-1D gases, but no validation against finite-range potentials or experimental parameters is provided.
  • ad hoc to paper The MCTDHB variational ansatz with a finite number M of orbitals yields the ground state accurately for all parameters shown.
    The truncation is not quantified (M is never reported), and the authors acknowledge code limitations for strong interactions, so the basis convergence is an unverified premise for the central claim.
  • standard math The rotating-frame Hamiltonian of Eq. (2) exactly represents the lab-frame rotating barrier via a unitary transformation.
    This is a standard transformation used throughout the paper; it is correct as stated, with the barrier now static in the rotating frame.
  • domain assumption The superfluid fraction defined by the energy derivative in Eq. (13) is the appropriate definition for a few-body system at zero temperature.
    Based on Leggett's definition of the superfluid fraction for a ring, which is standard in the literature, but it assumes the ground state responds adiabatically to the moving barrier.

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Cite this review

Pith. "Pith review of Superfluidity fraction of few bosons in an annular geometry in the presence of a rotating weak link." pith.science (2026). https://pith.science/paper/26ZWDPMT

@misc{pith2026190802351,
  author       = {Pith},
  title        = {Pith review of: Superfluidity fraction of few bosons in an annular geometry in the presence of a rotating weak link},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/26ZWDPMT}},
  note         = {Machine review of arXiv:1908.02351}
}
read the original abstract

We report a beyond mean-field calculation of mass current and superfluidity fraction for a system of few bosons confined in a ring geometry in the presence of a rotating weak link induced by a potential barrier. We apply the Multiconfiguration Hartree Method for bosons to compute the ground state of the system and show the average superfluidity fraction for a wide range of interaction strength and barrier height, highlighting the behavior of density correlation functions. The decrease of superfluidity fraction due to the increase of barrier height is found whereas the condensation fraction depends exclusively on the interaction strength, showing the independence of both phenomena.

Figures

Figures reproduced from arXiv: 1908.02351 by the authors.

Figure 2
Figure 2. FIG. 2. Phase profile of soliton solution for some values of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. (Color online) Energy per particle from GP equation [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Probability distribution for position(upper panel) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online) Ground state energy and current frac [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) Decrease of superfluidity fraction for different number of particles and interaction strength( [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Probability distribution of position(upper panel) and [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

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Reference graph

Works this paper leans on

46 extracted references · 40 canonical work pages

  1. [1]

    barriers split the image in four square blocks, with the darker regions (small normalized tunneling probabilities) located onxx′ < 0

    The density distribution vanishes forλ> 103 at the peak of the barrier inx = 0, despite there is just a slight increase on the width of the angular momentum distribution. barriers split the image in four square blocks, with the darker regions (small normalized tunneling probabilities) located onxx′ < 0. This is consistent with previous stud- ies in Ref. [...

    work page

  2. [2]

    I. M. Khalatnikov,An Introduction to the Theory of Su- perfluidity(Advanced Book Program, Perseus Publisher, New York, 1965)

    work page 1965

  3. [3]

    A. J. Leggett, J. Stat. Phys.93, 927 (1998)

    work page 1998

  4. [4]

    A. J. Leggett, Rev. Mod. Phys.71, S318 (1999)

    work page 1999

  5. [5]

    M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science269, 198 (1995)

    1995

  6. [6]

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

    work page 2008

  7. [7]

    Penrose and L

    O. Penrose and L. Onsager, Phys. Rev.104, 576 (1956)

    1956

  8. [8]

    V. F. Sears, E. C. Svensson, P. Martel, and A. D. B. Woods, Phys. Rev. Lett.49, 279 (1982)

    work page 1982

Show all 46 references
  1. [9]

    Raman, M

    C. Raman, M. Köhl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. 83, 2502 (1999)

    1999

  2. [10]

    C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett.99, 260401 (2007)

    2007

  3. [11]

    Ramanathan, K

    A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, Phys. Rev. Lett.106, 130401 (2011)

    2011

  4. [12]

    Clark and A

    J. Clark and A. I. Braginski, The SQUID Handbook (Wiley-VCH, Weinheim, 2004)

    2004

  5. [13]

    C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, Phys. Rev. Lett.111, 205301 (2013)

    2013

  6. [14]

    Albiez, R

    M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cris- tiani, and M. K. Oberthaler, Phys. Rev. Lett.95, 010402 (2005)

    2005

  7. [15]

    E. J. Mueller, Phys. Rev. A66, 063603 (2002)

    2002

  8. [16]

    Eckel, J

    S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London)506, 200 (2014)

    2014

  9. [17]

    Baharian and G

    S. Baharian and G. Baym, Phys. Rev. A 87, 013619 (2013)

    2013

  10. [18]

    Syafwan, P

    M. Syafwan, P. Kevrekidis, A. Paris-Mandoki, I. Lesanovsky, P. Krüger, L. Hackermüller, and H. Susanto, J. Phys. B: At. Mol. Opt. Phys.49, 235301 (2016)

    2016

  11. [19]

    K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Phys. Rev. A88, 063633 (2013)

    2013

  12. [20]

    Kunimi and I

    M. Kunimi and I. Danshita, Phys. Rev. A99, 043613 (2019)

    2019

  13. [21]

    Kumar, S

    A. Kumar, S. Eckel, F. Jendrzejewski, and G. K. Camp- bell, Phys. Rev. A95, 021602(R) (2017)

    2017

  14. [22]

    J. H. Kim, S. W. Seo, and Y. Shin, Phys. Rev. Lett.119, 185302 (2017)

    2017

  15. [23]

    Beattie, S

    S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadzibabic, Phys. Rev. Lett.110, 025301 (2013)

    2013

  16. [24]

    N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett.104, 030401 (2010)

    2010

  17. [25]

    Lopes, C

    R. Lopes, C. Eigen, N. Navon, D. Clément, R. P. Smith, and Z. Hadzibabic, Phys. Rev. Lett.119, 190404 (2017)

    2017

  18. [26]

    Chang, Q

    R. Chang, Q. Bouton, H. Cayla, C. Qu, A. Aspect, C. I. Westbrook, and D. Clément, Phys. Rev. Lett.117, 235303 (2016)

    2016

  19. [27]

    Navon, A

    N. Navon, A. L. Gaunt, R. P. Smith, and Z. Hadzibabic, Science 347, 167 (2015). 8

    2015

  20. [28]

    Naraschewski and R

    M. Naraschewski and R. J. Glauber, Phys. Rev. A59, 4595 (1999)

    1999

  21. [29]

    R. G. Dall, A. G. Manning, S. S. Hodgman, W. RuGway, K.V.Kheruntsyan,andA.G.Truscott,Nat.Phys. 9,341 (2013)

    2013

  22. [30]

    S. S. Hodgman, R. I. Khakimov, R. J. Lewis-Swan, A. G. Truscott, and K. V. Kheruntsyan, Phys. Rev. Lett.118, 240402 (2017)

    2017

  23. [31]

    O. E. Alon, A. I. Streltsov, and L. S. Cederbaum, Phys. Rev. A 77, 033613 (2008)

    2008

  24. [32]

    R. Roy, A. Gammal, M. C. Tsatsos, B. Chatterjee, B. Chakrabarti, and A. U. J. Lode, Phys. Rev. A 97, 043625 (2018)

    2018

  25. [33]

    A. U. J. Lode, B. Chakrabarti, and V. K. B. Kota, Phys. Rev. A 92, 033622 (2015)

    2015

  26. [34]

    J. H. V. Nguyen, M. C. Tsatsos, D. Luo, A. U. J. Lode, G. D. Telles, V. S. Bagnato, and R. G. Hulet, Phys. Rev. X 9, 011052 (2019)

    2019

  27. [35]

    Klaiman and L

    S. Klaiman and L. S. Cederbaum, Phys. Rev. A 94, 063648 (2016)

    2016

  28. [36]

    A. U. J. Lode, Phys. Rev. A93, 063601 (2016)

    2016

  29. [37]

    Fasshauer and A

    E. Fasshauer and A. U. J. Lode, Phys. Rev. A93, 033635 (2016)

    2016

  30. [38]

    Cominotti, D

    M. Cominotti, D. Rossini, M. Rizzi, F. Hekking, and A. Minguzzi, Phys. Rev. Lett.113, 025301 (2014)

    2014

  31. [39]

    Meyer, F

    H.-D. Meyer, F. Gatti, and G. A. Worth,Multidimen- sional Quantum Dynamics - MCTDH Theory and appli- cations (WILEY-VCH, Weinheim, 2009)

    2009

  32. [40]

    A. U. J. L. Lode, M. C. T. Tsatsos, E. Fasshauer, L. P. R. Lin, P. Molignini, C. Lévêque, and S. E. Weiner, MCTDH-X: The Time-dependent multiconfigurational Hartree for indistinguishable particles software, http: //ultracold.org, accessed: 2019-07-17

    2019

  33. [41]

    L. D. Carr, C. W. Clark, and W. P. Reinhardt, Phys. Rev. A 62, 063610 (2000)

    2000

  34. [42]

    J. Sato, R. Kanamoto, E. Kaminishi, and T. Deguchi, New J. Phys.18, 075008 (2016)

    2016

  35. [43]

    Muñoz Mateo, A

    A. Muñoz Mateo, A. Gallemí, M. Guilleumas, and R. Mayol, Phys. Rev. A91, 063625 (2015)

    2015

  36. [44]

    A. J. Leggett, Phys. Rev. Lett.25, 1543 (1970)

    1970

  37. [45]

    Sakmann, A

    K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Ceder- baum, Phys. Rev. A78, 023615 (2008)

    2008

  38. [46]

    X. Yin, Y. Hao, S. Chen, and Y. Zhang, Phys. Rev. A 78, 013604 (2008)

    2008

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