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REVIEW 3 major objections 4 minor 11 references

OpenMP Fortran programs for rotating dipolar Bose-Einstein condensates

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper presents OpenMP Fortran 90/95 programs that solve the time-dependent Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate in two and three dimensions.

desk verdict Useful OpenMP solvers for rotating dipolar BECs, but the 2D code's nonlinearity needs explicit confirmation and the paper lacks a converged benchmark. read the letter →

arxiv 2608.11278 v1 pith:KCPC4HEQ submitted 2026-08-11 cond-mat.quant-gas nlin.PS

Denis Mujo , Dušan Vudragović , Paulsamy Muruganandam , Sadhan K. Adhikari This is my paper · ORCID
classification cond-mat.quant-gasnlin.PS
keywords dipolarBose-EinsteincondensaterotatingGross-Pitaevskiiequationsplit-stepCrank-NicolsonOpenMPFortranvorticesLee-Huang-YanginteractionFFTsolver
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 presents two OpenMP Fortran 90/95 programs, imre3d-th.f90 and imre2dXY-th.f90, that solve the time-dependent Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate in three and two dimensions. The programs use a split-step semi-implicit Crank-Nicolson scheme with imaginary-time propagation for stationary states and real-time propagation for dynamics, and include optional Lee-Huang-Yang repulsion in 3D. The release responds to the 2022 observation of vortices and vortex stripes in a dipolar condensate, giving theorists a ready-made tool to study rotating dipolar systems. The paper also records that earlier 1D and 2D dipolar programs used three-dimensional dipolar nonlinearities by mistake, and that the arXiv versions of those programs corrected this.

What carries the argument

The split-step semi-implicit Crank-Nicolson scheme is the core algorithm: the time-dependent Gross-Pitaevskii equation is discretized in space and time, with the nonlocal dipolar term evaluated via fast Fourier transforms, and the resulting discretized equation is marched in imaginary or real time. Imaginary-time propagation drives an initial Gaussian (optionally seeded with a vortex phase via the FUNCTION and RANDOM parameters) to the stationary ground or vortex state; real-time propagation then evolves that state to give dynamics. Input parameters live in MODULEs GPE_DATA and COMM_DATA, and FFT grid sizes are chosen as powers of two for speed.

What would settle it

Open imre2dXY-th.f90 and check whether the dipolar potential is computed with the 2D kernel (e.g., the transverse integrated dipole-dipole interaction) or with the 3D kernel; then run the code with XDIPOLAR=0 and with a known analytical 2D non-rotating BEC ground state, and compare the dipolar energy term to a direct 2D quadrature. If the 2D program still evaluates a 3D nonlinearity, its 2D outputs are not solutions of the intended 2D equation.

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Extended reading notes

Core claim

The paper claims that its two new programs solve the time-dependent Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate: imre3d-th.f90 in three dimensions and imre2dXY-th.f90 in two dimensions. The 3D program optionally includes the repulsive Lee-Huang-Yang interaction, and both programs can switch off the dipolar part with XDIPOLAR=0, leaving a nondipolar rotating condensate. Stationary states come from imaginary-time propagation and dynamics from real-time propagation, both using the split-step semi-implicit Crank-Nicolson scheme. The paper also documents that some earlier 1D and 2D dipolar programs mistakenly used three-dimensional dipolar nonlinearities, with the arXiv versions of those papers already corrected.

Load-bearing premise

The 2D program uses the correct two-dimensional dipolar nonlinearity rather than the three-dimensional one that earlier 1D and 2D dipolar programs mistakenly used.

Editorial extensions

If this is right

  • Users can obtain stationary vortex states and real-time vortex dynamics of rotating dipolar BECs directly from the provided programs and example outputs.
  • Setting XDIPOLAR=0 lets the same solver reproduce nondipolar rotating condensate results, giving a built-in consistency check against the wider rotating-BEC literature.
  • In 3D, enabling LHY=1 extends the solver to rotating dipolar condensates with Lee-Huang-Yang quantum-fluctuation corrections.
  • The OpenMP parallelization and power-of-two FFT grids make parameter scans on multicore workstations practical.

Reading between the lines

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

  • Editorial inference: if the 2D program uses the correct 2D dipolar kernel, the earlier published 1D and 2D dipolar results computed with 3D kernels may need quantitative revision; the paper notes the error but does not explicitly confirm the fix in this release.
  • Editorial inference: the vortex-seeding parameters (FUNCTION, RANDOM) should allow direct numerical comparison with the vortex and vortex-stripe structures observed in the 2022 rotating dipolar BEC experiment, a test the authors do not report here.
  • Editorial inference: a natural next step would be MPI or GPU versions; the current OpenMP-only implementation is limited to shared-memory scaling within a single node.
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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

3 major / 4 minor

Summary. This manuscript is a CPC program summary submission describing the package DBEC-ROT-PROGRAM, which contains OpenMP Fortran 90/95 programs (imre3d-th.f90 and imre2dXY-th.f90) to solve the time-dependent Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate in three and two dimensions. The solution method is the split-step semi-implicit Crank-Nicolson scheme with imaginary- and real-time propagation for stationary states and dynamics, respectively. The paper also explains the operational details of the package, including input parameters, Makefiles, and the optional Lee-Huang-Yang term in 3D. A notable part of the 'Summary of revisions' is the admission that earlier 1D and 2D dipolar programs in Refs. [5,6,7] erroneously used 3D dipolar nonlinearities, with the parenthetical claim that the arXiv versions of those programs are correct.

Significance. If the programs are correct, this submission serves a timely community need: after the 2022 experimental observation of vortices in a rotating dipolar condensate, a publicly available, parallelized solver for the rotating dipolar Gross-Pitaevskii equation is a useful resource. The manuscript is also transparent about some past errors in earlier code versions, which is commendable. However, the paper provides no numerical validation of the central claim: the sample outputs are explicitly not fully converged, no comparison with published rotating dipolar BEC results is included, and the admitted prior error in the 2D dipolar nonlinearity is not explicitly stated to be fixed in the new 2D program. These issues directly affect the credibility of the advertised 2D capability, so the current text does not establish that the programs solve the intended equations. The strengths are the clear algorithmic summary, the availability of the code and Makefiles, and the OpenMP parallelization; the weakness is the absence of verification.

major comments (3)
  1. [Summary of revisions] The paper explicitly admits that the 1D and 2D dipolar programs in Refs. [5,6,7] 'erroneously used the 3D nonlinearities, in place of corresponding 1D and 2D nonlinearities, in numerical calculations.' However, it never states whether the new program imre2dXY-th.f90 in the present package uses the correct two-dimensional dipolar nonlinearity. Because imre2dXY-th.f90 is the direct successor of the erroneous 2D dipolar programs and the sample outputs are explicitly described as 'not fully converged numerically,' the manuscript does not currently establish that the 2D program solves the intended rotating dipolar Gross-Pitaevskii equation. Please add an explicit statement in the program description or readme.txt that identifies the dipolar term implemented in the 2D code, and provide a code-level check (e.g., the relevant subroutine) or a converged 2D test against a published rotating dipolar BEC result.
  2. [New version program summary / output] The 'Summary of revisions' states that the output examples 'are not fully converged numerically.' This is a serious omission for a program description paper, because the central claim is that the programs produce stationary states and real-time dynamics. Without at least one fully converged test case for both imre3d-th.f90 and imre2dXY-th.f90 (for example, the imaginary-time energy and chemical potential as functions of grid size and time step, compared with a known published value), a user cannot tell whether the algorithms and their implementations are correct. Please include such convergence tests in the output directory and report the resolved values in the manuscript.
  3. [Nature of problem / Solution method] The manuscript describes the problem and the solution method but does not specify how the dipolar term is discretized (for example, the use of FFT for the dipole-dipole convolution) or how the dipole orientation is defined in the 2D program. The text defers to Ref. [7] for details, but Ref. [7] is one of the references whose 2D nonlinearity is admitted to be wrong. The present manuscript should be self-contained about the 2D dipolar term so that readers and users can verify that the implementation matches the intended two-dimensional dipolar GP equation.
minor comments (4)
  1. [Summary of revisions] In the sentence about grid points, 'NX, NY in 2D and NX, NY, NZ in 2D and 3D' contains a repetition; it should read 'NX, NY in 2D and NX, NY, NZ in 3D'.
  2. [Summary of revisions] The word 'bipasses' should be 'bypasses'.
  3. [Reason for new version] The word 'consensates' should be 'condensates'.
  4. [New version program summary] The phrase 'withfftw3.f03 and fftw3.mod' is missing a space between 'with' and 'fftw3.f03'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper presents numerical solvers for an externally fixed equation and fits no parameters.

full rationale

The paper claims no physics derivation or prediction: it presents OpenMP Fortran programs that solve the time-dependent Gross-Pitaevskii equation for a rotating dipolar BEC using the split-step semi-implicit Crank-Nicolson scheme. The governing equation is specified by the problem statement and is external to the paper; the programs numerically integrate it, and the sample outputs are explicitly labeled as not fully converged. There is no fitted parameter later renamed as a prediction, no output defined in terms of an input by construction, and no load-bearing uniqueness theorem imported from the authors' prior work. The extensive self-citation is normal for a software-update paper: the new package is a modified version of previous programs, and the cited prior works describe the same numerical scheme and equation. The admitted error in earlier 1D/2D dipolar programs (that they used 3D nonlinearities) is a correctness or validation concern about the new 2D code, not a circularity: it does not make the present derivation equivalent to its inputs. The paper contains no internal chain in which a claimed result reduces to the assumption that produced it. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

No free parameters are fitted; the code has input parameters but they are user choices, not fitted constants. Three assumptions are load-bearing: the GP model, the numerical scheme, and the correction of the previously admitted dipolar nonlinearity error. No new entities are introduced.

assumptions (3)
  • domain assumption The time-dependent Gross-Pitaevskii equation with contact and dipolar interaction is the correct mean-field model for the rotating dipolar BEC systems addressed.
    The paper solves this equation directly without deriving or justifying the model; the whole code is built on it.
  • domain assumption Split-step semi-implicit Crank-Nicolson discretization with FFT evaluation of the dipolar term is stable and accurate for the chosen grid and time-step parameters.
    The paper relies on this standard numerical scheme; no error or convergence analysis is included.
  • ad hoc to paper The 2D rotating program uses the correct two-dimensional dipolar nonlinearity, not the three-dimensional form that the paper admits was used in previous 1D/2D dipolar programs.
    This is a correction-specific assumption for this code family; the paper never states explicitly that the fix is in place for the new 2D program.

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Cite this review

Pith. "Pith review of OpenMP Fortran programs for rotating dipolar Bose-Einstein condensates." pith.science (2026). https://pith.science/paper/KCPC4HEQ

@misc{pith2026260811278,
  author       = {Pith},
  title        = {Pith review of: OpenMP Fortran programs for rotating dipolar Bose-Einstein condensates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KCPC4HEQ}},
  note         = {Machine review of arXiv:2608.11278}
}
read the original abstract

In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 programs to solve the Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate (BEC) in two and three dimensions, which is a new version of our previous published programs for a dipolar Bose-Einstein condensate without rotation. After the recent experimental study of a rotating dipolar BEC [L. Klaus et al., Nature Phys. 18, 1453 (2022)], the present programs will be useful tools for related theoretical investigation. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary- and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version [L. E. Young-S. et al., Comput. Phys. Commun. 286 (2023) 108669].

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages

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    Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

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