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REVIEW 3 major objections 3 minor 73 references

The paper argues that rigid rotation does not qualitatively modify the weak Bose-Einstein condensation of a magnetized charged Bose gas; rotation only changes quantitative thermodynamics and shifts the magnetic response from diamagnetic tow

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2026-08-03 09:46 UTC pith:2P7UAHSE

load-bearing objection A timely question, a competent formalism, and a load-bearing sign error that kills the QGP numerics. the 3 major comments →

arxiv 2607.29297 v1 pith:2P7UAHSE submitted 2026-07-31 hep-ph nucl-th

Weak Bose-Einstein condensation in a rigidly rotating magnetized charged Bose gas

E. Siri , N. Sadooghi This is my paper
classification hep-ph nucl-th
keywords weak Bose-Einstein condensationLandau quantizationrigid rotationmagnetorotational fugacityTolman-Ehrenfest temperaturediamagnetism-paramagnetism crossovercharged Bose gasquark-gluon plasma
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks whether rigid rotation changes the way charged bosons condense in a strong magnetic field. Its answer is that rotation does not qualitatively alter the weak Bose-Einstein condensation scenario: the system never develops a sharp critical temperature, the magnetorotational fugacity stays below one across the physically relevant temperatures, and the specific heat remains smooth. Instead, rotation modifies thermodynamic quantities quantitatively, entering through the Tolman-Ehrenfest local temperature, and it shifts the magnetic response—magnetic fields favor diamagnetism while rotation pushes the gas toward paramagnetism. A sympathetic reader would care because this determines whether pion-like condensates in rotating neutron stars and in heavy-ion collision fireballs remain in the diffuse condensation regime or acquire a real phase transition.

Core claim

For a noninteracting charged scalar gas subject to a constant magnetic field and rigid rotation, the authors construct the finite-temperature thermodynamic potential in the nonrelativistic lowest-Landau-level approximation. By modifying the effective chemical potential they define a magnetorotational fugacity z_B,Ω, and within the high-temperature approximation rotation appears in the thermodynamics only through the Tolman-Ehrenfest local temperature. They find that z_B,Ω < 1 throughout the relevant temperature ranges, that the ground-state population fills gradually, and that the specific heat has no singularity—three signatures that the weak, diffuse BEC scenario induced by Landau quantiza

What carries the argument

The central object is the magnetorotational fugacity z_B,Ω = exp[β(μ_B − NΩ)] for the lowest Landau level, with μ_B = μ − √(m² + eB) and N the Landau degeneracy; it replaces the ordinary fugacity and encodes both magnetic quantization and rotation. The argument rests on two devices: the replacement of the angular-momentum sum over ℓ by the degeneracy N, which makes the explicit NΩ term cancel from the density-fixing equation, and the Tolman-Ehrenfest factor Γ(v) = 1/√(1−v²), which converts the lab temperature into the local corotating temperature. With these, the LLL thermodynamic potential becomes proportional to the polylogarithm Li_{3/2}(z_B,Ω), the density to Li_{1/2}(z_B,Ω), and all the

Load-bearing premise

The load-bearing step is treating the angular-momentum sum as the Landau degeneracy N, a replacement the text justifies by βΩ ≪ 1 but which actually requires β(N+n)Ω ≪ 1; for the plotted neutron-star parameters (N = 10^4 and βΩ up to ~0.03) this product is of order 300, so the LLL potential, density, and fugacity used to draw the conclusions are not under control in that regime, and the same problem appears in the assumption μ_B < 0 versus the density-fixing solution μ_B ≈ NΩ

What would settle it

Compute the density-fixed fugacity and thermodynamic potential by evaluating the ℓ-summation in the paper's Eq. (II.29) exactly, without replacing it by N, for the NS parameters of Figs. 1(b)–11 (N = 10^4, 10^−4 ≤ t ≤ 0.1, βΩ up to ~0.03). If z_B,Ω ever reaches or exceeds unity, or the logarithm in the potential turns negative or ill-defined, then the claim that rotation leaves the weak BEC scenario intact fails in precisely the regime where the paper claims it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • In the quark-gluon plasma parameter regime, the gas remains in the weak-condensation regime with no sharp BEC transition, but rotation visibly raises pressure, energy density, and angular-momentum density through the Tolman correction.
  • In the neutron-star parameter regime, rotational corrections are numerically negligible across the plotted temperature range, so the weak condensation scenario is effectively the same as for a purely magnetized gas.
  • The characteristic temperature t_{3/4} at which ground-state population falls to 75% decreases with rotation, meaning rotation suppresses the low-momentum accumulation—an analogue of inverse magnetorotational catalysis.
  • The magnetization crossover implies a measurable magnetic response: for sufficiently fast rotation and weak magnetic field, a QGP-like charged boson gas behaves paramagnetically, while stronger fields restore diamagnetism.
  • The absence of a specific-heat peak provides a clean observational test to distinguish weak BEC from strong BEC in rotating magnetized environments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Because rotation enters only through the Tolman-Ehrenfest local temperature in this approximation, the predicted paramagnetic tendency should be interpreted as a gradient effect, not a direct Ω coupling; testing this would require a calculation that goes beyond the high-temperature LLL truncation.
  • The relation χ_f = T I/N² linking free susceptibility to moment of inertia is a compact prediction of the LLL framework; it could be checked independently by numerical evaluation of the exact ℓ-sum, and it suggests a general fluctuation-response pattern for rotating magnetized gases.
  • If the weak-BEC conclusion survives the uncontrolled βNΩ approximation, an analogue experiment with rotating ultracold atoms in a synthetic magnetic field could look for the same diamagnetic-to-paramagnetic crossover at small N, where the approximation is controllable.
  • The paper's robustness claim should not be extrapolated to interacting pion condensates without further work: self-interactions or higher Landau levels could reintroduce rotational effects that are absent in the noninteracting LLL limit.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper studies a noninteracting charged Bose gas in a constant magnetic field and rigid rotation, using the generalized Fock-Schwinger formalism in the nonrelativistic and lowest-Landau-level approximations. A modified effective chemical potential leads to a 'magnetorotational fugacity' z_{B,Ω}, and the authors claim that rigid rotation does not qualitatively alter the weak BEC scenario induced by Landau quantization: z_{B,Ω}<1, no specific-heat singularity, and a gradual ground-state population are presented as signatures. The thermodynamic potential, density, fugacity, and all subsequent thermodynamic quantities are derived from the LLL potential (II.35). Numerical results are given for QGP and neutron-star parameters, including pressure, magnetization, susceptibilities, moment of inertia, and speed of sound.

Significance. If the derivation were sound, the paper would provide a useful extension of the weak-BEC scenario to rotating magnetized bosons and give a concrete prediction for QGP and neutron-star matter. The analytic expressions for the angular-momentum density, magnetization, and response functions are systematic and cover a broad set of observables. However, the central results rest on an expansion that is not valid in the QGP parameter regime used for the main figures, and the neutron-star parameters are internally inconsistent. These issues directly affect the paper's principal claim that rotation does not change the qualitative weak-BEC picture.

major comments (3)
  1. [§II.B, Eq. (II.27)–(II.35) and §III, Eq. (III.14)–(III.15)] The derivation of the LLL potential uses ln(1−x)=−Σ x^j/j with x = z_{B,Ω}^{(0)} e^{−βω} e^{βμ_ℓ}. After the shift μ_ℓ→μ_ℓ−μ_Ω, the maximum of x occurs at ω=0, ℓ=N and equals e^{βμ_B}. The text assumes μ_B<0 before Eq. (II.27), but the density-fixing solution (III.14) gives μ_B = NΩ − πT D^{−2}, D≡2πρ0 λ_B/(eB0)−ζ(1/2). For QGP parameters (e.g. t=0.2, b=1, ρ=0.28, v=0.5), NΩ≈0.236 GeV while πT D^{−2}≈10^{−3} GeV, so μ_B is positive and βμ_B≈8.4. Thus |x_max|≫1 and the expansion (II.28) diverges; Eqs. (II.35), (III.3), and (III.15) are mathematically undefined in the plotted QGP regime. The statement z_{B,Ω}<1 is insufficient: the expansion parameter for the highest angular-momentum state is z_{B,Ω} e^{βNΩ}=e^{βμ_B}.
  2. [§II.B, Eq. (II.32)] The replacement Σ_{ℓ=−n}^{N−n} e^{βjμ_ℓ} ≈ (1/Ω)∫ dμ e^{βjμ} ≈ N requires both βj(N−n)Ω and βjnΩ to be much smaller than unity for all contributing n. For the QGP parameters used in Figs. 1–13 (t=0.2, v=0.5, R=10 fm), βΩ≈0.7 and with N=24 one obtains βNΩ≈17; the integral is then dominated by e^{βjNΩ}/(βjΩ), not by N. Hence the LLL potential, the density (III.3), and the fugacity (III.15) inherit an uncontrolled approximation in the QGP regime. The same problem affects the HLL contribution in (II.36).
  3. [Table I and Sec. V] The neutron-star parameters are internally inconsistent. Using Eq. (II.20) with N=10^4 and b=0.03 gives S=2πN/(eB0)≈1.07×10^8 GeV^{−2}, corresponding to R≈1.2×10^{−11} m, whereas Table I lists R=10 km. Conversely, R=10 km with b=0.03 gives N≈7.6×10^{34}. The figures use N=10^4 together with v=RΩ for R=10 km, which cannot hold simultaneously. This ambiguity affects the validity condition βNΩ≪1 for Eq. (II.32) and all N-dependent observables such as j (IV.4), I (IV.12), and κ_T (IV.16). The authors must specify which cylinder radius is actually used and recompute N consistently.
minor comments (3)
  1. [Eq. (II.36)] The HLL term contains a prefactor '2B0T' that appears dimensionally inconsistent with the LLL term (II.35); presumably it should be eB0T/(2πλ_B) times a sum over n. Please clarify the prefactor and the definition of z_{B,Ω}^{(n)} for n>0.
  2. [§IV, Eqs. (IV.1)–(IV.2)] The thermodynamic derivatives are defined at different fixed variables, e.g., j is taken at fixed v but v=RΩ, so varying Ω while keeping v fixed is unusual. Please state the independent variables explicitly and define whether Ω or v is held fixed in each derivative.
  3. [Fig. 7 and general notation] The contour plots in Fig. 7 use a grayscale without a visible color bar; the labels 'Paramagnetic' and 'Diamagnetic' are clear, but a legend for the contour values would improve readability. Also, the symbol ξ_{3/4} in Fig. 5(b) is later used for the anisotropy ζ_aniso; please avoid this clash.

Circularity Check

2 steps flagged

The headline magnetorotational fugacity z_B,Ω<1 and the claim that rotation enters only through the Tolman temperature are built into the ad hoc subtraction μ_ℓ → μ_ℓ − μ_Ω; the weak-BEC signature is partly constructed rather than independently derived.

specific steps
  1. self definitional [Sec. IIB Eq. (II.25)-(II.27); Sec. III Eq. (III.15); Sec. V text before Fig. 1]
    "At this stage, we need to define an appropriate cutoff to ensure that the argument of the logarithm function appearing in (II.25) remains positive. To do this, we modify μℓ by replacing it with μℓ − μΩ, where μΩ ≡(N−n)Ω. ... Introducing the 'magnetorotational fugacity', z^{(n)}_{B,Ω} ≡e^{β(μ_B−μ_Ω)}. ... As mentioned in Sec. III, the dependence of Ω from the term NΩ in z_{B,Ω} cancels out due to the regularization method we used to derive z_{B,Ω} from (III.15). ... In this approximation, z_{B,Ω}<1 for all values of T, as expected."

    The magnetorotational fugacity is defined only after subtracting μΩ=(N−n)Ω, with the explicit purpose of keeping the logarithm's argument positive. Therefore z_B,Ω<1 and the cancellation of the explicit Ω-dependence are properties inserted by the definition, not outcomes of the physics. The paper itself states that the Ω-dependence cancels 'due to the regularization method' and must be reintroduced by hand through the Tolman factor. The central weak-BEC signature 'z_B,Ω<1' and the headline conclusion 'rotation enters solely through the Tolman-Ehrenfest local temperature' are thus consequences of the chosen regulator, not independent predictions.

  2. other [Sec. IIB Eq. (II.27)-(II.28) vs Sec. III Eq. (III.14)]
    "Assuming that μ_B <0 and noting that ω is always positive for n∈N_0, we can conclude that the remaining exponential satisfies e^{β(μℓ−μΩ)} ≤1 for all values of ℓ∈ {−n, N−n}. ... μ≃NΩ + m_B −πT(2πρ0λB/eB0 −ζ(1/2))^{−2}."

    The log-expansion in (II.28) is valid only for |x|<1, and the text secures this by assuming μ_B<0. But the density-fixing solution (III.14), derived from the resulting LLL potential, gives μ_B=μ−m_B≈NΩ>0 for the plotted parameters (e.g., NS: N=10^4, βΩ≈0.03 at t=10^-4, so βμ_B≈300). The maximum x in the sum is e^{βμ_B}≫1, so the expansion diverges exactly in the regime where Φ_LLL, n_th, and z_B,Ω are evaluated. The claimed z_B,Ω<1 is therefore extracted from a series whose convergence condition is contradicted by the predicted chemical potential; the weak-BEC signature is an artifact of this self-referential convergence assumption rather than an independent result.

full rationale

The paper does not rest on a load-bearing self-citation chain: Refs. [7,8] by the same authors supply methodology and comparative limits, and the underlying no-transition weak-BEC physics is inherited from the external analysis of magnetized bosons in Refs. [2,3]. The derivation is largely self-contained in setting up the Fock-Schwinger propagator and the thermodynamic potential. However, the central quantitative signature of the paper — the magnetorotational fugacity remaining below unity — is partly circular. The subtraction μ_ℓ → μ_ℓ − μ_Ω is introduced ad hoc to make the logarithm well-defined, and z_B,Ω is then defined with that same subtraction; the result z_B,Ω<1 and the claim that rotation only enters through the Tolman temperature follow from this construction, as the paper explicitly admits when it says the Ω-dependence cancels 'due to the regularization method' and is reintroduced by hand. A further internal inconsistency — the convergence assumption μ_B<0 versus the derived μ_B≈NΩ>0 — makes the LLL expansion divergent for the plotted phenomenology, reinforcing that the headline weak-BEC signatures are not independently established. Because the qualitative conclusion also relies on the independent external weak-BEC framework, the circularity is partial rather than total, giving a score of 6.

Axiom & Free-Parameter Ledger

2 free parameters · 8 axioms · 1 invented entities

The central quantitative structure depends on several uncontrolled choices: the angular-momentum sum approximation, the sign assumption on μ_B, the Tolman-temperature substitution, and the hand-fixed p0. None of these are benchmarked against independent results or data.

free parameters (2)
  • Ground-state momentum cutoff p0 = p0≈0.997 mπ (QGP), 0.073 mπ (NS)
    Chosen by imposing n_gr(t=1.5)=0.75ρ for QGP and n_gr(t=0.1)=0.75ρ for NS; the 75% fraction is a hand-chosen anchor.
  • Condensate fraction 0.75 used to define t3/4 = 0.75
    Defines the moment when the ground-state population reaches 75% of total density; arbitrary but claimed not to affect qualitative conclusions.
axioms (8)
  • domain assumption Nonrelativistic approximation ω_B ≈ m_B + k_z²/2m_B + eB n/m_B (II.24)
    Restricts the calculation to low momenta/temperatures; stated in Sec. IIB.
  • domain assumption Lowest Landau level approximation; HLL and antiparticles neglected
    The weak-BEC analysis in Sec. III and most thermodynamic results in Secs. IV-V use only the LLL particle sector.
  • ad hoc to paper Replacement of the ℓ-sum by N in Eq. (II.32) under βΩ≪1
    The derivation actually requires β(N+n)Ω≪1; for NS parameters (N=10^4, βΩ~0.03 at t=10^-4) the condition is violated, so the resulting thermodynamic potential is not established there.
  • ad hoc to paper Assumption μ_B<0 in Sec. II to keep log arguments positive
    Contradicted by Eq. (III.14), which gives μ_B≈NΩ>0 for the plotted QGP regime; the highest-ℓ LLL mode then has Boltzmann weight >1 and the grand-canonical log can become negative.
  • domain assumption Tolman-Ehrenfest local temperature T → Γ(v)T
    Used to reinsert Ω dependence after it cancels from z_BΩ; assumes local equilibrium at the boundary radius R with v=RΩ<1.
  • standard math Polylog asymptotic Li_{1/2}(e^{-α}) ≈ sqrt(π/α)+ζ(1/2) for α≪1 (III.12)
    Standard expansion; used to invert the fixed-density equation for μ.
  • domain assumption Global charge neutrality is not imposed
    Explicitly stated in the Introduction; differs from charged-pion condensation literature such as Refs. [50,51].
  • domain assumption Rigid rotation metric and vierbein (II.2)-(II.3)
    Standard corotating-frame description of a uniformly rotating cylinder.
invented entities (1)
  • Magnetorotational fugacity z_BΩ no independent evidence
    purpose: Unified bookkeeping variable combining μ_B, m_B, and NΩ to parametrize LLL thermodynamics and diagnose weak BEC
    A definition rather than a new physical object; its rotational dependence is largely absorbed by the ad hoc μΩ shift and reinserted through the Tolman temperature.

pith-pipeline@v1.3.0-daily-deepseek · 28425 in / 24375 out tokens · 255846 ms · 2026-08-03T09:46:59.725716+00:00 · methodology

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read the original abstract

We investigate the weak Bose-Einstein condensation (BEC) scenario of a noninteracting charged Bose gas simultaneously subjected to a strong magnetic field and rigid rotation. Using standard methods of finite-temperature quantum field theory and the generalized Fock-Schwinger formalism, we derive the corresponding thermodynamic potential in the nonrelativistic and lowest Landau level approximations. An appropriate modification of the effective chemical potential yields a consistent thermodynamic description and naturally introduces a magnetorotational fugacity. Within the high-temperature approximation, rigid rotation enters the thermodynamics solely through the Tolman-Ehrenfest local temperature. We demonstrate that rigid rotation does not qualitatively modify the weak BEC scenario induced by Landau quantization. The magnetorotational fugacity remains below unity throughout the phenomenologically relevant temperature range, while the continuous evolution of the ground state population and the absence of a singularity in the specific heat provide complementary signatures of the persistence of weak BEC. We further study the thermodynamic properties of the system under conditions relevant to quark-gluon plasma and neutron-star matter. We show that rotational effects are much more pronounced in the former. Our analysis reveals a new magnetic response to rigid rotation: while magnetic fields enhance diamagnetism, rotation drives it toward paramagnetism. This behavior reflects a competition between magnetic quantization and rotational orbital motion, emphasizing the role of rotation in shaping the magnetic response of bosonic matter.

Figures

Figures reproduced from arXiv: 2607.29297 by E. Siri, N. Sadooghi.

Figure 1
Figure 1. Figure 1: FIG. 1. Panel a: The temperature ( [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The temperature ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The dependence of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. In panel (a) and (b) contour plots [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Panel a: The [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: (d). Additionally, RΩ is insignificant enough that it does not affect the magnetic properties of the medium. It is important to emphasize that the conclusion drawn above, particularly regarding the effect of the magnetic field, is based on the approximations made in this pa￾per. These results are consistent with findings presented in [3], which discuss the effect of magnetic fields on the thermodynamics of… view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Panel a: The [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Panel a: The [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Panel a: The [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗

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Reference graph

Works this paper leans on

73 extracted references · 61 linked inside Pith

  1. [1]

    In- stead, the system exhibits a diffuse phase transition over specific temperature intervals

    A critical temperature cannot be defined. In- stead, the system exhibits a diffuse phase transition over specific temperature intervals. In this situa- tion, bosons tend to concentrate around the ground state, contrasting the strong BEC scenario. 1 For simplicity, we omit the superscript(0)onz (0) B,Ω that appears in (II.35). 5

  2. [2]

    The fugacity remains less than1at all tempera- tures

  3. [3]

    para- magnetic

    There is no peak in the specific heat of the Bose gas. In the present paper, we discuss a scenario where, aside fromtheinfluenceofB, thesystemisinastateofrigidro- tation. We observe that a similar weak scenario arises in thiscontext. Todemonstratethis, letusfirstsetz B,Ω = 1 in (III.3). Utilizing Liν(1) =ζ(ν), whereζ(ν)represents the Riemann zeta function...

  4. [4]

    However, whenΩ̸= 0, we expectc 2 s <2andc s ̸=c ph. In Fig. 10(b), thebdependence ofc s is demonstrated for fixedRΩ = 0.25, ρ= 0.28, t= 0.8, andrset to r= 7andr= 10. It is important to note that larger values forrcorrespond to an increase in the degener- acy factorN. Our observations reveal thatc s decreases 15 RΩ 0.25 RΩ 0.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0...

  5. [5]

    V. P. Gusynin, V. A. Miransky and I. A. Shovkovy,Di- mensional reduction and catalysis of dynamical symme- try breaking by a magnetic field, Nucl. Phys. B462, 249 (1996), [arXiv:hep-ph/9509320 [hep-ph]]

    Pith/arXiv arXiv 1996

  6. [6]

    Perez Rojas,Bose-Einstein condensation may occur in a constant magnetic field, Phys

    H. Perez Rojas,Bose-Einstein condensation may occur in a constant magnetic field, Phys. Lett. B379, 148–152 (1996), [arXiv:hep-th/9510191 [hep-th]]

    Pith/arXiv arXiv 1996

  7. [7]

    Castillo Ayón, G

    A. Castillo Ayón, G. Gil Perez, A. Pérez Martínez, H. Pérez Rojas, G. Piccinelli Bocchi, A. E. Rodríguez Concepción and A. Sanchez,Magnetized charged boson gas and two-step condensation in neutron-star matter, Phys. Rev. C113, 015802 (2026)

    2026

  8. [8]

    A. Dohi, H. Liu, T. Noda and M. a. Hashimoto,Cooling of isolated neutron stars with pion condensation: Possible fast cooling in a low-symmetry energy model, Int. J. Mod. Phys. E31, 2250006 (2022), [arXiv:2112.13302 [astro- ph.HE]]

    Pith/arXiv arXiv 2022

  9. [9]

    Ayala, M

    A. Ayala, M. Loewe, J. C. Rojas and C. Villavicencio, Magnetic catalysis of a charged Bose-Einstein conden- sate, Phys. Rev. D86, 076006 (2012), [arXiv:1208.0390 18 [hep-ph]]

    Pith/arXiv arXiv 2012

  10. [10]

    Ayala, P

    A. Ayala, P. Mercado and C. Villavicencio,Magnetic catalysis of a finite size pion condensate, Phys. Rev. C 95, 014904 (2017), [arXiv:1609.02595 [hep-ph]]

    Pith/arXiv arXiv 2017

  11. [11]

    Siri and N

    E. Siri and N. Sadooghi,Thermodynamic properties of a relativistic Bose gas under rigid rotation, Phys. Rev. D 110, 036016 (2024), [arXiv:2405.09481 [hep-ph]]

    Pith/arXiv arXiv 2024

  12. [12]

    Siri and N

    E. Siri and N. Sadooghi,Bose-Einstein condensation in a rigidly rotating relativistic boson gas, Phys. Rev. D111, 036011 (2025), [arXiv:2411.12581 [hep-ph]]

    Pith/arXiv arXiv 2025

  13. [13]

    Siri and N

    E. Siri and N. Sadooghi,Spontaneous breaking of global U(1) symmetry in an interacting Bose gas under rigid rotation, [arXiv:2508.17055 [hep-ph]]

    Pith/arXiv arXiv

  14. [14]

    J. L. Noronha and I. A. Shovkovy, Color-flavor locked superconductor in a magnetic field, Phys. Rev. D76, 105030 (2007) [erratum: Phys. Rev. D86, 049901 (2012)] [arXiv:0708.0307 [hep-ph]]

    Pith/arXiv arXiv 2007

  15. [15]

    Fayazbakhsh and N

    S. Fayazbakhsh and N. Sadooghi,Phase diagram of hot magnetized two-flavor color superconducting quark mat- ter, Phys. Rev. D83, 025026 (2011), [arXiv:1009.6125 [hep-ph]]

    Pith/arXiv arXiv 2011

  16. [16]

    Preis, A

    F. Preis, A. Rebhan and A. Schmitt,Inverse magnetic catalysis in dense holographic matter, JHEP03, 033 (2011), [arXiv:1012.4785 [hep-th]]

    Pith/arXiv arXiv 2011

  17. [17]

    G. S. Bali, F. Bruckmann, G. Endrödi, Z. Fodor, S. D. Katz, S. Krieg, A. Schäfer and K. K. Szabo,The QCD phase diagram for external magnetic fields, JHEP 02, 044 (2012), [arXiv:1111.4956 [hep-lat]]

    Pith/arXiv arXiv 2012

  18. [18]

    Fayazbakhsh, S

    S. Fayazbakhsh, S. Sadeghian and N. Sadooghi,Proper- ties of neutral mesons in a hot and magnetized quark mat- ter, Phys. Rev. D86, 085042 (2012), [arXiv:1206.6051 [hep-ph]]

    Pith/arXiv arXiv 2012

  19. [19]

    Bruckmann, G

    F. Bruckmann, G. Endrödi and T. G. Kovacs,Inverse magnetic catalysis and the Polyakov loop, JHEP04, 112 (2013), [arXiv:1303.3972 [hep-lat]]

    Pith/arXiv arXiv 2013

  20. [20]

    Fayazbakhsh and N

    S. Fayazbakhsh and N. Sadooghi,Weak decay constant of neutral pions in a hot and magnetized quark matter, Phys. Rev. D88, 065030 (2013), [arXiv:1306.2098 [hep- ph]]

    Pith/arXiv arXiv 2013

  21. [21]

    E. J. Ferrer, V. de la Incera and X. J. Wen,Quark antiscreening at strong magnetic field and inverse mag- netic catalysis, Phys. Rev. D91, 054006 (2015), [arXiv:1407.3503 [nucl-th]]

    Pith/arXiv arXiv 2015

  22. [22]

    Fayazbakhsh and N

    S. Fayazbakhsh and N. Sadooghi,Anomalous magnetic moment of hot quarks, inverse magnetic catalysis, and reentrance of the chiral symmetry broken phase, Phys. Rev. D90, 105030 (2014), [arXiv:1408.5457 [hep-ph]]

    Pith/arXiv arXiv 2014

  23. [23]

    Hattori and X

    K. Hattori and X. G. Huang,Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions, Nucl. Sci. Tech.28, 26 (2017), [arXiv:1609.00747 [nucl- th]]

    Pith/arXiv arXiv 2017

  24. [24]

    Adhikari, M

    P. Adhikari, M. Ammon, S. S. Avancini, A. Ayala, A. Bandyopadhyay, D. Blaschke, F. L. Braghin, P. Buiv- idovich, R. P. Cardoso and C. Cartwright,et al.,Strongly interacting matter in extreme magnetic fields, Prog. Part. Nucl. Phys.146, 104199 (2026), [arXiv:2412.18632 [nucl- th]]

    Pith/arXiv arXiv 2026

  25. [25]

    Yamamoto and Y

    A. Yamamoto and Y. Hirono,Lattice QCD in ro- tating frames, Phys. Rev. Lett.111, 081601 (2013), [arXiv:1303.6292 [hep-lat]]

    Pith/arXiv arXiv 2013

  26. [26]

    V. E. Ambruş and E. Winstanley,Rotating quan- tum states, Phys. Lett. B734, 296–301 (2014), [arXiv:1401.6388 [hep-th]]

    Pith/arXiv arXiv 2014

  27. [27]

    V. E. Ambruş and E. Winstanley,Rotating fermions in- side a cylindrical boundary, Phys. Rev. D93, 104014 (2016), [arXiv:1512.05239 [hep-th]]

    Pith/arXiv arXiv 2016

  28. [28]

    Jiang and J

    Y. Jiang and J. Liao,Pairing phase transitions of mat- ter under rotation, Phys. Rev. Lett.117, 192302 (2016), [arXiv:1606.03808 [hep-ph]]

    Pith/arXiv arXiv 2016

  29. [29]

    Ebihara, K

    S. Ebihara, K. Fukushima and K. Mameda,Boundary effects and gapped dispersion in rotating fermionic mat- ter, Phys. Lett. B764, 94–99 (2017), [arXiv:1608.00336 [hep-ph]]

    Pith/arXiv arXiv 2017

  30. [30]

    M. N. Chernodub and S. Gongyo,Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics, JHEP01, 136 (2017), [arXiv:1611.02598 [hep-th]]

    Pith/arXiv arXiv 2017

  31. [31]

    M. N. Chernodub and S. Gongyo,Effects of rotation and boundaries on chiral symmetry breaking of rela- tivistic fermions, Phys. Rev. D95, 096006 (2017), [arXiv:1702.08266 [hep-th]]

    Pith/arXiv arXiv 2017

  32. [32]

    X. Wang, M. Wei, Z. Li and M. Huang,Quark matter under rotation in the NJL model with vector interaction, Phys. Rev. D99, 016018 (2019), [arXiv:1808.01931 [hep- ph]]

    Pith/arXiv arXiv 2019

  33. [34]

    V. V. Braguta, M. N. Chernodub, A. A. Roenko and D. A. Sychev,Negative moment of inertia and rotational instability of gluon plasma, Phys. Lett. B852, 138604 (2024), [arXiv:2303.03147 [hep-lat]]

    Pith/arXiv arXiv 2024

  34. [35]

    K. K. Pradhan, B. Sahoo, D. Sahu and R. Sahoo,Ther- modynamics of a rotating hadron resonance gas with van der Waals interaction, Eur. Phys. J. C84, 936 (2024), [arXiv:2304.05190 [hep-ph]]

    Pith/arXiv arXiv 2024

  35. [36]

    V. V. Braguta, M. N. Chernodub, I. E. Kudrov, A. A. Roenko and D. A. Sychev,Negative Barnett ef- fect, negative moment of inertia of the gluon plasma, and thermal evaporation of the chromomagnetic conden- sate, Phys.Rev.D110, 014511(2024), [arXiv:2310.16036 [hep-ph]]

    Pith/arXiv arXiv 2024

  36. [37]

    Morales-Tejera, V

    S. Morales-Tejera, V. E. Ambruş and M. N. Chernodub, Firewall boundaries and mixed phases of rotating quark matter in linear sigma model, Phys. Rev. D112, 054031 (2025), [arXiv:2502.19087 [nucl-th]]

    arXiv 2025

  37. [38]

    M. A. Ahadi and N. Sadooghi,Chiral vortical conductivi- ties and the moment of inertia of a rigidly rotating Fermi gas, Phys. Rev. D111, 116011 (2025), [arXiv:2502.19264 [hep-ph]]

    Pith/arXiv arXiv 2025

  38. [39]

    Singha, S

    P. Singha, S. Busuioc, V. E. Ambruş and M. N. Chern- odub,Linear sigma model with quarks and Polyakov loop in rotation: Phase diagrams, Tolman-Ehrenfest law, and mechanical properties, Phys. Rev. D112, 094031 (2025), [arXiv:2503.17291 [nucl-th]]

    Pith/arXiv arXiv 2025

  39. [40]

    Mameda and A

    K. Mameda and A. Yamamoto,Magnetism and rotation in relativistic field theory, PTEP2016, 093B05 (2016), [arXiv:1504.05826 [hep-th]]

    Pith/arXiv arXiv 2016

  40. [41]

    H.L.Chen, K.Fukushima, X.G.HuangandK.Mameda, Analogy between rotation and density for Dirac fermions in a magnetic field, Phys. Rev. D93, 104052 (2016), [arXiv:1512.08974 [hep-ph]]

    Pith/arXiv arXiv 2016

  41. [42]

    Liu and I

    Y. Liu and I. Zahed,Rotating Dirac fermions in a mag- netic field in 1+2 and 1+3 dimensions, Phys. Rev. D98, 014017 (2018), [arXiv:1710.02895 [hep-ph]]

    Pith/arXiv arXiv 2018

  42. [43]

    Sadooghi, S

    N. Sadooghi, S. M. A. Tabatabaee Mehr and F. Taghi- navaz,Inverse magnetorotational catalysis and the phase diagram of a rotating hot and magnetized quark mat- ter, Phys. Rev. D104, 116022 (2021), [arXiv:2108.12760 [hep-ph]]. 19

    Pith/arXiv arXiv 2021

  43. [44]

    H. M. Ghalati and N. Sadooghi,Magnetic dual chiral density wave phase in rotating cold quark matter, Phys. Rev. D108, 054032 (2023), [arXiv:2306.04472 [nucl-th]]

    Pith/arXiv arXiv 2023

  44. [45]

    Fukushima, K

    K. Fukushima, K. Hattori and K. Mameda,Preponderant orbital polarization in relativistic magnetovortical matter, Phys. Rev. Lett.135, 011601 (2025), [arXiv:2409.18652 [hep-ph]]

    Pith/arXiv arXiv 2025

  45. [46]

    Skokov, A

    V. Skokov, A. Y. Illarionov and V. Toneev,Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A24, 5925–5932 (2009), [arXiv:0907.1396 [nucl-th]]

    Pith/arXiv arXiv 2009

  46. [47]

    W. T. Deng and X. G. Huang,Event-by-event generation of electromagnetic fields in heavy-ion collisions, Phys. Rev. C85, 044907 (2012), [arXiv:1201.5108 [hep-ph]]

    Pith/arXiv arXiv 2012

  47. [48]

    Jiang, Z

    Y. Jiang, Z. W. Lin and J. Liao,Rotating quark-gluon plasma in relativistic heavy ion collisions, Phys. Rev. C 94, 044910 (2016), [arXiv:1602.06580 [hep-ph]]

    Pith/arXiv arXiv 2016

  48. [49]

    L.Adamczyket al.[STAR],GlobalΛhyperon polarization in nuclear collisions: evidence for the most vortical fluid, Nature548, 62–65 (2017), [arXiv:1701.06657 [nucl-ex]]

    Pith/arXiv arXiv 2017

  49. [50]

    Becattini and M

    F. Becattini and M. A. Lisa,Polarization and vorticity in the quark–gluon plasma, Ann. Rev. Nucl. Part. Sci.70, 395–423 (2020), [arXiv:2003.03640 [nucl-ex]]

    Pith/arXiv arXiv 2020

  50. [51]

    R. C. Duncan and C. Thompson,Formation of very strongly magnetized neutron stars: Implications for gamma-ray bursts, Astrophys. J. Lett.392, L9 (1992)

    1992

  51. [52]

    Q. H. Peng and H. Tong,The physics of strong magnetic fields in neutron stars, Mon. Not. Roy. Astron. Soc.378, 159 (2007), [arXiv:0706.0060 [astro-ph]]

    Pith/arXiv arXiv 2007

  52. [53]

    V. M. Kaspi and A. Beloborodov,Magnetars, Ann. Rev. Astron. Astrophys.55, 261–301 (2017), [arXiv:1703.00068 [astro-ph.HE]]

    Pith/arXiv arXiv 2017

  53. [54]

    Liu and I

    Y. Liu and I. Zahed,Pion condensation by rotation in a magnetic field, Phys. Rev. Lett.120, 032001 (2018), [arXiv:1711.08354 [hep-ph]]

    Pith/arXiv arXiv 2018

  54. [55]

    Bai and L

    P. Bai and L. He,Absence of charged pion condensation in a magnetic field with parallel rotation, Phys. Rev. D 113, no. 7, 074016 (2026), [arXiv:2512.07473 [nucl-th]]

    Pith/arXiv arXiv 2026

  55. [56]

    T. Guo, J. Li, C. Mu and L. He,Formation of a super- giant quantum vortex in a relativistic Bose-Einstein con- densate driven by rotation and a parallel magnetic field, Phys. Rev. D106, 094010 (2022), [arXiv:2111.13159 [nucl-th]]

    Pith/arXiv arXiv 2022

  56. [57]

    Guo and Y

    T. Guo and Y. Xiao,Quantum vortex phases of charged pion condensates induced by rotation in a magnetic field, Phys. Rev. D109, 056024 (2024), [arXiv:2402.04475 [hep-ph]]

    Pith/arXiv arXiv 2024

  57. [58]

    D. N. Voskresensky,Charged pion vortices in rotating systems, Phys. Part. Nucl. Lett.21, 1036–1044 (2024), [arXiv:2404.16904 [nucl-th]]

    Pith/arXiv arXiv 2024

  58. [59]

    D. N. Voskresensky,Pion condensation at rotation in magnetic field, electric, and scalar potential wells, Phys. Rev. D111, 036022 (2025), [arXiv:2410.12392 [hep-ph]]

    Pith/arXiv arXiv 2025

  59. [60]

    Cao and L

    G. Cao and L. He,Rotation induced charged pion con- densation in a strong magnetic field: A Nambu–Jona- Lasinio model study, Phys. Rev. D100, 094015 (2019), [arXiv:1910.02728 [nucl-th]]

    Pith/arXiv arXiv 2019

  60. [61]

    H. L. Chen, X. G. Huang and K. Mameda,Do charged- pions condense in a magnetic field with rotation?, JHEP 02, 216 (2024), [arXiv:1910.02700 [nucl-th]]

    Pith/arXiv arXiv 2024

  61. [62]

    Kumar, D

    A. Kumar, D. Gaur and V. Chandra,Rotating magne- tized pion gas of finite transverse size: condensation con- straints and transport properties, [arXiv:2606.20530 [hep- ph]]

    Pith/arXiv arXiv

  62. [63]

    R. C. Tolman,On the weight of heat and thermal equilib- rium in general relativity, Phys. Rev.35(1930) 904

    1930

  63. [64]

    Tolman and P

    R. Tolman and P. Ehrenfest,Temperature equilibrium in a static gravitational field, Phys. Rev.36, (1930) 1791

    1930

  64. [65]

    J. I. Kapusta and C. Gale, Finite Temperature Field Theory, Principles and Applications, 2nd ed. (Cambridge University Press, Cambridge, England, 2006)

    2006

  65. [66]

    M. N. Chernodub,Inhomogeneous confining-deconfining phases in rotating plasmas, Phys. Rev. D103, 054027 (2021), [arXiv:2012.04924 [hep-ph]

    Pith/arXiv arXiv 2021

  66. [67]

    I. A. Rather, U. Rahaman, V. Dexheimer, A. A. Usmani and S. K. Patra,Heavy magnetic neutron stars, Astro- phys. J.917, 46 (2021), [arXiv:2104.05950 [nucl-th]]

    Pith/arXiv arXiv 2021

  67. [68]

    K. K. Pradhan, D. Sahu, C. R. Singh and R. Sahoo, Bose-Einstein condensation and dissipative dynamics in a relativistic pion gas, Phys. Rev. D112, 074031 (2025), [arXiv:2212.09288 [hep-ph]]

    arXiv 2025

  68. [69]

    Becattini, I

    F. Becattini, I. Karpenko, M. Lisa, I. Upsal and S. Voloshin,Global hyperon polarization at local ther- modynamic equilibrium with vorticity, magnetic field and feed-down,Phys. Rev. C95, 054902 (2017), arXiv:1610.02506 [nucl-th]

    Pith/arXiv arXiv 2017

  69. [70]

    Nasser Tawfik and H

    A. Nasser Tawfik and H. Magdy,Hadronic equation of state and speed of sound in thermal and dense medium, Int. J. Mod. Phys. A29, 1450152 (2014), [arXiv:1206.0901 [hep-ph]]

    Pith/arXiv arXiv 2014

  70. [71]

    E. J. Ferrer, V. de la Incera, J. P. Keith, I. Portillo and P. L. Springsteen,Equation of state of a dense and mag- netized fermion system, Phys. Rev. C82, 065802 (2010), [arXiv:1009.3521 [hep-ph]]

    Pith/arXiv arXiv 2010

  71. [72]

    Sadooghi and S

    N. Sadooghi and S. M. A. Tabatabaee,Paramagnetic squeezing of a uniformly expanding quark-gluon plasma in and out of equilibrium, Phys. Rev. D99, 056021 (2019), [arXiv:1901.06928 [nucl-th]]

    Pith/arXiv arXiv 2019

  72. [73]

    Kiamari, N

    M. Kiamari, N. Sadooghi and M. S. Jafari,Relativis- tic magnetohydrodynamics of a spinful and vortical fluid: Entropy current analysis, Phys. Rev. D109, 036024 (2024), [arXiv:2310.01874 [nucl-th]]

    Pith/arXiv arXiv 2024

  73. [74]

    Kiamari and N

    M. Kiamari and N. Sadooghi,Wigner function of a rigidly rotating and magnetized QED plasma, [arXiv:2509.03440 [nucl-th]]. 20

    arXiv