Crossover from weak to strong quench in a spinor Bose-Einstein condensate

Deokhwa Hong; Joon Hyun Kim; Seji Kang; Yong-il Shin

REVIEW 3 major objections 4 minor 39 references

Crossover from weak to strong quench in a spinor Bose-Einstein condensate

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Quenching a spin-1 antiferromagnetic Bose-Einstein condensate from the easy-plane to the easy-axis polar phase produces a crossover in early spin dynamics that matches the momentum-dependent Bogoliubov instability of the initial state…

desk verdict A solid experimental test of the weak-to-strong quench crossover in a spinor BEC; the seeded-sample probe is genuinely clever, but the q̃ calibration (scattering length and effective density) is the hinge and deserves sharper treatment. read the letter →

arxiv 1909.00681 v2 pith:PLS52PD4 submitted 2019-09-02 cond-mat.quant-gas

Seji Kang , Deokhwa Hong , Joon Hyun Kim , Yong-il Shin This is my paper · ORCID

classification cond-mat.quant-gas PACS 03.75.Mn

keywords spinorBose-EinsteincondensatequantumquenchdynamicinstabilityBogoliubovtheoryantiferromagneticspin-1easy-planepolarstatespindomainformationstrength

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 reports experiments on a sodium-23 spin-1 antiferromagnetic Bose-Einstein condensate quenched from the easy-plane polar (EPP) phase to the easy-axis polar (EAP) phase by suddenly reversing the sign of the quadratic Zeeman energy. It argues that the early-time post-quench dynamics is set by the momentum-dependent Bogoliubov instability of the initial EPP state, and that the character of this instability changes with the dimensionless quench strength $\tilde{q}=q_f/(c_2 \bar{n})$: for $\tilde{q}<1$ the most unstable mode is at zero momentum, for $1<\tilde{q}<2$ a finite wavenumber dominates, and for $\tilde{q}>2$ the zero-momentum mode becomes stable, suppressing long-wavelength spin excitations. Using a sample seeded with a small condensate population in the $m_z=0$ component, the authors show that the zero-momentum seed loses its influence for $\tilde{q}>2$, confirming the predicted disappearance of the long-wavelength instability. If correct, this establishes a quantitative connection between quench dynamics and linear stability analysis in a spinor condensate, and it maps out distinct weak, intermediate, and strong quench regimes that govern defect and pattern formation in these systems.

What carries the argument

The load-bearing object is the transverse magnon branch of the easy-plane polar state, with energy $E_t(k)=\sqrt{(\epsilon_k - q)(\epsilon_k - q + 2c_2 n)}$, where $\epsilon_k=\hbar^2 k^2/2m$ is the single-particle energy and $c_2 n$ the spin interaction energy. After the quench to $q>0$ this energy becomes imaginary for a range of wavenumbers, making the corresponding modes dynamically unstable; the maximum imaginary part gives the growth rate $\Gamma(\tilde{q})$. As $\tilde{q}$ increases, the unstable momentum region changes topology: for $\tilde{q}<1$ it is a disk centered at $k=0$, for $1<\tilde{q}<2$ the most unstable mode moves to $k_m=k_s\sqrt{\tilde{q}-1}$, and for $\tilde{q}>2$ the $k=0$ mode becomes stable so the unstable region is an annulus with $k_m>\xi_s^{-1}$. This momentum-space topology change is the mechanism the paper identifies as the origin of the crossover in the observed spin dynamics.

What would settle it

An experiment that measured the momentum-resolved growth of density modulations in the $m_z=0$ component after the quench (for example, by Fourier analysis of absorption images) and found significant low-wavenumber growth for $\tilde{q}>2$, or a seeded sample whose early dynamics still accelerates at those quenches, would falsify the claim that the zero-momentum mode has stabilized.

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Extended reading notes

Core claim

The central claim is that the crossover from weak to strong quench in the EPP-to-EAP transition is governed by the momentum dependence of the transverse magnon dispersion of the initial easy-plane polar state. For $\tilde{q}<1$, the most unstable mode is the zero-momentum magnon, producing long-wavelength spin excitations and irregular spin domains; for $1<\tilde{q}<2$, the most unstable wavenumber becomes $k_m=k_s\sqrt{\tilde{q}-1}$, and the early spin texture appears granulated or array-like; for $\tilde{q}>2$, the $k=0$ mode is no longer unstable, the unstable region in momentum space becomes an annulus, and the pattern turns speckled. The decisive experiment uses a seeded sample with an enhanced $m_z=0$ condensate fraction, i.e., enhanced zero-momentum transverse magnons: the seed accelerates and makes coherent the early growth of $\eta$ (the $m_z=0$ fraction) for low $\tilde{q}$, but its effect monotonically fades with increasing $\tilde{q}$ and nearly vanishes for $\tilde{q}>2$, in agreement with the prediction that the zero-momentum mode has stabilized. The authors conclude that the observed crossover is consistent with the Bogoliubov description of the dynamic instability of the initial spinor condensate.

Load-bearing premise

The claim rests on the calibration of the quench strength $\tilde{q}$ using a specific scattering length and an averaged density; if that calibration is off, the crossover positions shift and the quantitative match to Bogoliubov theory breaks down.

Editorial extensions

If this is right

For $\tilde{q}>2$, the composite-defect nucleation picture (domain walls bounded by half-quantum vortices) that holds in the weak-quench regime no longer applies; the small domain size makes hosting $m_z=\pm1$ cores energetically prohibitive, so defect formation in strong quenches must be described by a different mechanism.
The reverse quench (EAP to EPP) should exhibit the same crossover behavior as a function of the initial excitation energy, because the two phases share the same magnon dispersion structure; this is directly predicted by the paper.
The seeded-sample protocol provides a selective amplifier for zero-momentum magnons, offering a practical tool to probe the stability of the $k=0$ mode and to calibrate spin-interaction parameters in spinor condensates.
The three identified quench regimes (weak, intermediate, strong) give a classification that future experiments on quench-induced pattern formation in spinor gases should respect when comparing to theory.

Reading between the lines

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

The seeded-sample technique could be developed into a momentum-resolved quench spectroscopy: by preparing seeds at different wavenumbers, one could map out the full imaginary branch of the magnon dispersion, directly imaging the unstable momentum region and its topology change at $\tilde{q}=1$ and $\tilde{q}=2$.
A quantitative comparison with numerical simulations that include nonlinear interactions beyond the linear-growth stage would test whether the Bogoliubov picture survives into the late-time dynamics, especially in the strong-quench regime where the most unstable mode has single-particle character.
If the suppression of long-wavelength modes at high $\tilde{q}$ holds generally, it implies that quench dynamics in this system cannot be described by a universal scaling with a single length scale (e.g., the spin healing length); instead the dynamics selects a characteristic scale set by $k_m^{-1}$, which may have implications for the interpretation of early-time scaling laws in other symmetry-br

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You should know this one. The paper is a careful experimental study of the EPP-to-EAP quench in a spin-1 sodium BEC, and it does something new: it sweeps the dimensionless quench strength q̃ from 0.12 to 4.4 and shows the early-time dynamics crossing over from long-wavelength instability (irregular domains) to short-wavelength, speckled structures, with the long-wavelength instability strongly suppressed for q̃>2. The seeded-sample experiment—preparing a condensate with a deliberately enhanced m_F=0 component—is a genuinely clever way to test the stability of the k=0 mode. The amplitude of the collective spin oscillation decreases with q̃ and vanishes above q̃~2, which is a direct, qualitative confirmation of the Bogoliubov prediction.

The theory is not new (Lamacraft 2007, Matuszewski 2010), and the paper doesn't pretend otherwise. No free parameters are fitted. The imaging and the η(t) curves are consistent with the instability picture.

The soft spot is the calibration. The dimensionless quench strength is q̃=q_f/(c2 n̄), and the paper changed the sodium scattering length from 0.823 a0 (used in their earlier work) to 1.88 a0, citing Knoop et al. That's a factor 2.28. If the old value were right, every data point would sit below q̃=2 and the claimed suppression of the k=0 mode would vanish. They also use an effective density n̄=2/3 n0, the linear axial average, whereas a density-weighted average for a TF profile would give 4/5 n0—a 20% shift in all q̃ values. They say the density factor was verified by spin-sound measurements, but the reference is an unpublished arXiv preprint, and Fig. 5 shows no error bars on t1 and t2, so the comparison against Γ^{-1}(q̃) doesn't bound the calibration uncertainty. They are upfront about the imaging resolution limit in footnote 1, which is why the intermediate-regime comparison stays qualitative.

None of this is an internal contradiction. The qualitative crossover is real, and the central argument—that the early-time dynamics is governed by the momentum-dependent instability of the initial state—holds up. But the specific thresholds q̃~1 and q̃>2 are only as solid as the calibration. A referee should push for a sensitivity analysis or at least a more transparent discussion of the uncertainty in as and n̄.

For the spinor-BEC community, this is a useful, citable experimental result. I'd send it to peer review; it deserves careful refereeing, and with reasonable revisions on the calibration, it's publishable. Not a home run, but a solid advance.

Referee Report

3 major / 4 minor

Summary. The paper reports an experimental study of the early-time dynamics of a quasi-two-dimensional spin-1 antiferromagnetic 23Na Bose-Einstein condensate after a sudden quench from the easy-plane polar (EPP) phase to the easy-axis polar (EAP) phase. The authors introduce the dimensionless quench strength q̃ = qf/(c2 n̄) and observe that the spatial scale of the initially generated mz = 0 spin domains decreases with increasing q̃, with an array-like pattern appearing for q̃ around unity and a speckled pattern for q̃ > 2. They also prepare a "seeded" sample containing a residual mz = 0 population to selectively enhance zero-momentum spin excitations, and show that the resulting early enhancement—a collective spin oscillation and a reduced onset time t1—weakens with increasing q̃ and nearly disappears for q̃ > 2. The observations are interpreted as consistent with the Bogoliubov dynamic instability of the initial EPP state, in which the k = 0 transverse mode is unstable only for q̃ < 2 and the most unstable mode acquires finite momentum for q̃ > 1.

Significance. If the calibration of q̃ is sound, the experiment provides a clear qualitative confirmation of the Bogoliubov picture across three quench regimes, and the seeded-sample experiment is a direct, falsifiable test of the predicted stabilization of the k = 0 mode for q̃ > 2. A notable strength is that no free parameters are fitted to force agreement: the theory curve comes from the standard Bogoliubov dispersion, and the experimental variation is controlled by the same q̃ parameter. The result would be a useful benchmark for spinor-BEC quench dynamics and supports the idea of using quenches as a magnon thermometer. However, the central quantitative claims are threshold statements in q̃, and the comparison is only as solid as the calibration of q̃ through the scattering length and the effective density; this is where the manuscript currently needs the most work.

major comments (3)

[Sec. III and Fig. 5] The quantitative quench-strength axis is q̃ = qf/(c2 n̄), and every threshold claim (the crossover at q̃ ≈ 1 and the stabilization of k = 0 for q̃ > 2) is stated in these units. The two inputs to q̃ are not accompanied by uncertainty or sensitivity analysis: as = 1.88 a0 in footnote 2 is a factor 2.28 larger than the value used in the authors' previous work, and the effective-density factor n̄ = 2/3 n0 rests on the unpublished Ref. [23]. A shift in either input moves the q̃ = 1 and q̃ = 2 boundaries and could eliminate the strong-quench regime entirely. In addition, the quoted range 0.12 < q̃ < 4.4 is internally inconsistent with c2 n0 = h × 30.7 Hz and n̄ = 2/3 n0, since qf/h = 82 Hz gives q̃ = 4.0. The authors should provide error bars for t1 and t2 in Fig. 5 and propagate calibration uncertainties through the comparison with the theoretical growth rate.
[Sec. IV.C and Fig. 5] The caption of Fig. 5 states that the solid green line is Γ^(-1)(q̃), but Γ(q̃) is defined in Sec. II as the maximum growth rate over momentum, which is constant for 1 < q̃ < 2. The seeded-sample comparison in Sec. IV.C is instead made against Im[Et(k = 0)] ∝ sqrt(q̃(2 − q̃)), which decreases to zero at q̃ = 2. These two quantities have different q̃-dependence between q̃ = 1 and q̃ = 2, so the legend must specify which curve is actually plotted. As printed, the reader cannot verify the claimed agreement of the seeded t1 data with the k = 0 growth rate.
[Sec. IV.C] For the seeded sample, η(t) exhibits a large-amplitude collective oscillation during the early stage, and t1 is defined as the first time at which η = 0.2. If this crossing occurs while η is still following the oscillatory pulse rather than the exponential instability growth, then t1 is not a direct measure of the k = 0 growth rate and the comparison with Im[Et(k = 0)] is not justified. The authors should show, for example by fitting the exponential envelope or by identifying that the crossing occurs in the post-pulse growth stage, that the seeded t1 values are set by the instability growth rate and not by the seed-induced oscillation.

minor comments (4)

[Abstract and Sec. III] The abstract says the quench strength is varied 'up to 4', while Sec. III states the range as 0.12 < q̃ < 4.4; these numbers should be reconciled after the calibration issue is resolved.
[Fig. 3 caption] The middle image in Fig. 3 is said to show 'the same data shown in Fig. 1(c)', but the corresponding data appear in Fig. 2(c); the cross-reference should be corrected.
[Sec. IV.B] The phrase 'free from a proportional factor' for the Γ^(-1) curve in Fig. 5 is unclear; it should be replaced by an explicit statement of the vertical normalization used when overlaying t1 on the inverse growth rate.
[Sec. III] The claim that n̄ = 2/3 n0 is 'experimentally verified' via the spin-sound measurement relies on Ref. [23], which is an unpublished preprint; the verification should be described in enough detail for the reader to judge the density-averaging procedure, or an independent calibration should be provided.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the Bogoliubov predictions come from external theory, and the q̃ calibration rests on independent scattering-length and spin-sound measurements, not on the quench data.

full rationale

The paper's central claim is that the early-time post-quench dynamics crosses over from long-wavelength to short-wavelength instability as q̃ increases, consistent with the Bogoliubov dispersion of the initial EPP state. This is an experimental test of an external theory (Refs. [10,15,16]), not a derivation from the data. No parameter is fitted to the quench data: q̃ is computed from the independently controlled quadratic Zeeman energy qf, the scattering-length-based spin interaction coefficient c2 (as = 1.88 a0 from Ref. [21], confirmed in Refs. [22,23]), and the effective density n̄ = 2/3 n0. The effective-density factor is justified by the standard Thomas-Fermi averaging in Refs. [25,26] and by the authors' separate spin-sound measurement in Ref. [23]; that self-citation is independent experimental evidence, not a fit to the present crossover data, so it does not raise the circularity score. In Fig. 5, the comparison uses Γ^{-1}(q̃) 'free from a proportional factor,' and t1 and t2 are measured rather than adjusted. The seeded-sample experiment in Sec. IV.C directly tests the k = 0 stability prediction for q̃ > 2 instead of assuming it. Calibration uncertainties in as or n̄ would shift the q̃ axis and are a legitimate correctness risk, but they are not a logical circularity because the theory curve is not constructed from the outcome it is compared with.

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

The central claim rests on standard mean-field and Bogoliubov descriptions of spinor BECs, plus specific modeling choices for effective density and seed interpretation. No free parameters are fitted; the dimensionless quench strength is computed from independently measured quantities, though with calibration uncertainty.

assumptions (5)

domain assumption The mean-field Bogoliubov description of the spin-1 BEC (with two magnon branches) applies to the experimental sample, and the unstable modes grow exponentially with the predicted rates.
Sec. II uses the EPP magnon dispersion from Refs [10,15,16] to predict the most unstable modes; the experiment assumes this linearized theory describes the early-time dynamics.
domain assumption The effective 2D density n̄ = (2/3)n0, obtained by averaging the parabolic Thomas-Fermi profile along the axial direction, determines the spin dynamics.
Sec. III uses n̄ to compute ξs and q̃; the sample thickness 2Rz ~ 4 µm is comparable to the spin healing length 3.3 µm, so the 2D approximation is not exact.
domain assumption The residual mz=0 population in the seeded sample acts as a zero-momentum transverse magnon seed, selectively enhancing long-wavelength excitations.
Sec. IV C interprets the faster onset and collective oscillations in the seeded sample as evidence for enhanced low-k magnon population.
domain assumption The quench from q<0 to qf>0 is instantaneous on the timescale of spin dynamics.
The experiment changes q suddenly (presumably within a few ms); the exact ramp time is not stated.
domain assumption The spin temperature is equilibrated after the 0.6 s holding in the EPP phase, so the initial fluctuations reflect the equilibrium state.
Sec. III states the sample's spin temperature is assumed equilibrated after holding.

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Cite this review

Pith. "Pith review of Crossover from weak to strong quench in a spinor Bose-Einstein condensate." pith.science (2026). https://pith.science/paper/PLS52PD4

@misc{pith2026190900681,
  author       = {Pith},
  title        = {Pith review of: Crossover from weak to strong quench in a spinor Bose-Einstein condensate},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PLS52PD4}},
  note         = {Machine review of arXiv:1909.00681}
}

abstract

We investigate the early-time dynamics of a quasi-two-dimensional spin-1 antiferromagnetic Bose-Einstein condensate after a sudden quench from the easy-plane to the easy-axis polar phase. The post-quench dynamics shows a crossover behavior as the quench strength $\tilde{q}$ is increased, where $\tilde{q}$ is defined as the ratio of the initial excitation energy per particle to the characteristic spin interaction energy. For a weak quench of $\tilde{q}<1$, long-wavelength spin excitations are dominantly generated, leading to the formation of irregular spin domains. With increasing $\tilde{q}$, the length scale of the initial spin excitations decreases, and we demonstrate that the long-wavelength instability is strongly suppressed for high $\tilde{q}>2$. The observed crossover behavior is found to be consistent with the Bogoliubov description of the dynamic instability of the initial spinor condensate.

Figures

Figures reproduced from arXiv: 1909.00681 by the authors.

**Figure 2.** FIG. 2. Phase-transition dynamics of an antiferromagnetic BEC from the EPP to the EAP phase. (a) Optical density (OD) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Example images showing an array-like spatial pat [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. Time evolutions of the fractional population [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5. Characterization of the growth curve of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. Images of the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

39 extracted references · 35 canonical work pages

[23]

J. H. Kim, D. H. Hong, and Y. Shin, Observa- tion of two sound modes in a binary superﬂuid gas, arXiv:1907.10289

work page Pith review arXiv 1907
[1]

Polkovnikov, K

A. Polkovnikov, K. Sengupta, A. Silva, and M. Ven- galattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011). 7

work page 2011
[2]

Eisert, M

J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many- body systems out of equilibrium, Nat. Phys. 11, 124 (2015)

2015
[3]

Heyl, Dynamical quantum phase transition: a review, Rep

M. Heyl, Dynamical quantum phase transition: a review, Rep. Prog. Phys. 81, 054001 (2018)

work page 2018
[4]

E. M. Bookjans, A. Vinit, and C. Raman, Quantum Phase Transition in an Antiferromagnetic Spinor Bose- Einstein Condensate, Phys. Rev. Lett. 107, 195306 (2011)

work page 2011
[5]

S. Kang, S. W. Seo, J. H. Kim, and Y. Shin, Emergence and scaling of spin turbulence in quenched antiferromag- netic spinor BECs, Phys. Rev. A 95, 053638 (2017)

work page 2017
[6]

Vinit and C

A. Vinit and C. Raman, Precise measurements on a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates, Phys. Rev. A 95, 011603(R) (2017)

work page 2017
[7]

S. Kang, S. W. Seo, H. Takeuchi, and Y. Shin, Ob- servation of wall-vortex composite defects in a spinor Bose-Einstein condensate, Phys. Rev. Lett. 122, 095301 (2019)

work page 2019

Show all 39 references

[8]

Ho, Spinor Bose Condensates in Optical Traps, Phys

T.-L. Ho, Spinor Bose Condensates in Optical Traps, Phys. Rev. Lett. 81, 742 (1998)

1998
[9]

Ohmi and K

T. Ohmi and K. Machida, Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, J. Phys. Soc. Jpn. 67, 1822 (1998)

1998
[10]

Kawaguchi and M

Y. Kawaguchi and M. Ueda, Spinor Bose-Einstein con- densates, Phys. Rep. 520, 253 (2012)

2012
[11]

Zhou, Spin Correlation and Discrete Symmetry in Spinor Bose-Einstein Condensates, Phys

F. Zhou, Spin Correlation and Discrete Symmetry in Spinor Bose-Einstein Condensates, Phys. Rev. Lett. 87, 080401 (2001)

2001
[12]

Zhou, Quantum spin nematic states in Bose-Einstein condensates, Int

F. Zhou, Quantum spin nematic states in Bose-Einstein condensates, Int. J. Mod. Phys. B 17, 2643 (2003)

2003
[13]

N. T. Phuc, Y. Kawaguchi, and M. Ueda, Fluctuation- induced and symmetry-prohibited metastabilities in spinor Bose-Einstein condensates, Phys. Rev. A 88, 043629 (2013)

2013
[14]

S. W. Seo, S. Kang, W. J. Kwon, and Y. Shin, Half- Quantum Vortices in an Antiferromagnetic Spinor Bose- Einstein Condensate, Phys. Rev. Lett. 115, 015301 (2015)

2015
[15]

Lamacraft, Quantum Quenches in a Spinor Conden- sate, Phys

A. Lamacraft, Quantum Quenches in a Spinor Conden- sate, Phys. Rev. Lett. 98, 160404 (2007)

2007
[16]

Matuszewski, Rotonlike Instability and Pattern For- mation in Spinor Bose-Einstein Condensates, Phys

M. Matuszewski, Rotonlike Instability and Pattern For- mation in Spinor Bose-Einstein Condensates, Phys. Rev. Lett. 105, 020405 (2010)

2010
[17]

L. M. Symes, D. Baillie, and P. B. Blakie, Static structure factors for a spin-1 Bose-Einstein condensate, Phys. Rev. A 89, 053628 (2014)

2014
[18]

J. H. Kim, D. H. Hong, S. Kang, and Y. Shin, Metastable hard-axis polar state of a spinor Bose-Einstein conden- sate under a magnetic ﬁeld gradient, Phys. Rev. A 99, 023606 (2019)

2019
[19]

Gerbier, A

F. Gerbier, A. Widera, S. F¨ olling, O. Mandel, and I. Bloch, Resonant control of spin dynamics in ultracold quantum gases by microwave dressing, Phys. Rev. A 73, 041602(R) (2006)

2006
[20]

L. Zhao, J. Jiang, T. Tang, M. Webb, and Y. Liu, Dy- namics in spinor condensates tuned by a microwave dress- ing ﬁeld, Phys. Rev. A 89, 023608 (2014)

2014
[21]

Knoop, T

S. Knoop, T. Schuster, R. Scelle, A. Trautmann, J. App- meier, and M. K. Oberthaler, Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium, Phys. Rev. A 83, 042704 (2011)

2011
[22]

Bienaim´ e, E

T. Bienaim´ e, E. Fava, G. Colzi, C. Mordini, S. Seraﬁni, C. Qu, S. Stringari, G. Lamporesi, and G. Ferrari, Spin- dipole oscillation and polarizability of a binary Bose- Einstein condensate near the miscible-immiscible phase transition, Phys. Rev. A 94, 063652 (2016)

2016
[24]

A. T. Black, E. Gomez, L. D. Turner, S. Jung, and P. D. Lett, Spinor Dynamics in an Antiferromagnetic Spin-1 Condensate, Phys. Rev. Lett. 99, 070403 (2007)

2007
[25]

Stringari, Dynamics of Bose-Einstein condensed gases in highly deformed traps, Phys

S. Stringari, Dynamics of Bose-Einstein condensed gases in highly deformed traps, Phys. Rev. A 58, 2385 (1998)

1998
[26]

Zaremba, Sound propagation in a cylindrical Bosec- ondensed gas, Phys

E. Zaremba, Sound propagation in a cylindrical Bosec- ondensed gas, Phys. Rev. A 57, 518 (1998)

1998
[27]

Klempt, O

C. Klempt, O. Topic, G. Gebreyesus, M. Scherer, T. Hen- ninger, P. Hyllus, W. Ertmer, L. Santos, and J. J. Arlt, Multiresonant Spinor Dynamics in a Bose-Einstein Con- densate, Phys. Rev. Lett. 103, 195302 (2009)

2009
[28]

Scherer, B

M. Scherer, B. Lucke, G. Gebreyesus, O. Topic, F. Deuretzbacher, W. Ertmer, L. Santos, J. J. Arlt, and C. Klempt, Spontaneous Breaking of Spatial and Spin Symmetry in Spinor Condensates, Phys. Rev. Lett. 105, 135302 (2010)

2010
[29]

Stenger, S

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Mies- ner, A. P. Chikkatur, and W. Ketterle, Spin domains in ground-state Bose-Einstein condensates, Nature (Lon- don) 396, 345 (1998)

1998
[30]

Jim´ enez-Garc´ ıa, A

K. Jim´ enez-Garc´ ıa, A. Invernizzi, B. Evrard, C. Frapolli, J. Dalibard and F. Gerbier, Spontaneous formation and relaxation of spin domains in antiferromagnetic spin-1 condensates, Nat. Commun. 10, 1442 (2019)

2019
[31]

Takeuchi (private communication)

H. Takeuchi (private communication)
[32]

L. M. Symes, D. Baillie, and P. B. Blakie, Dynamics of a quenched spin-1 antiferromagnetic condensate in a harmonic trap, Phys. Rev. A 98, 063618 (2018)

2018
[33]

Fujimoto and M

K. Fujimoto and M. Tsubota, Spin turbulence in a trapped spin-1 spinor Bose-Einstein condensate, Phys. Rev. A 85, 053641 (2012)

2012
[34]

M. Karl, B. Nowak, and T. Gasenzer, Tuning universality far from equilibrium, Sci. Rep. 3, 2394 (2013)

2013
[35]

Witkowska, T

E. Witkowska, T. ´Swislocki, and M. Matuszewski, Ther- mal ﬂuctuations and quantum phase transition in anti- ferromagnetic Bose-Einstein condensates, Phys. Rev. A 90, 033604 (2014)

2014
[36]

Fujimoto and M

K. Fujimoto and M. Tsubota, Direct and inverse cascades of spin-wave turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates, Phys. Rev. A 93, 033620 (2016)

2016
[37]

L. A. Williamson, and P. B. Blakie, Universal Coarsening Dynamics of a Quenched Ferromagnetic Spin-1 Conden- sate, Phys. Rev. Lett. 116, 025301 (2016)

2016
[38]

Schmied, T

C.-M. Schmied, T. Gasenzer, P. B. Blakie, Violation of single-length scaling dynamics via spin vortices in an iso- lated spin-1 Bose gas, arXiv:1904.13222 (2019)

2019 arXiv
[39]

Mel´ e-Messeguer, B

M. Mel´ e-Messeguer, B. Juli´ a-D´ ıaz, A. Polls, and L. San- tos, Thermal spin ﬂuctuations in spinor Bose-Einstein condensates, Phys. Rev. A 87, 033632 (2013)

2013

Pith tools

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

[1] [23]

J. H. Kim, D. H. Hong, and Y. Shin, Observa- tion of two sound modes in a binary superﬂuid gas, arXiv:1907.10289

work page Pith review arXiv 1907

[2] [1]

Polkovnikov, K

A. Polkovnikov, K. Sengupta, A. Silva, and M. Ven- galattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011). 7

work page 2011

[3] [2]

Eisert, M

J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many- body systems out of equilibrium, Nat. Phys. 11, 124 (2015)

2015

[4] [3]

Heyl, Dynamical quantum phase transition: a review, Rep

M. Heyl, Dynamical quantum phase transition: a review, Rep. Prog. Phys. 81, 054001 (2018)

work page 2018

[5] [4]

E. M. Bookjans, A. Vinit, and C. Raman, Quantum Phase Transition in an Antiferromagnetic Spinor Bose- Einstein Condensate, Phys. Rev. Lett. 107, 195306 (2011)

work page 2011

[6] [5]

S. Kang, S. W. Seo, J. H. Kim, and Y. Shin, Emergence and scaling of spin turbulence in quenched antiferromag- netic spinor BECs, Phys. Rev. A 95, 053638 (2017)

work page 2017

[7] [6]

Vinit and C

A. Vinit and C. Raman, Precise measurements on a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates, Phys. Rev. A 95, 011603(R) (2017)

work page 2017

[8] [7]

S. Kang, S. W. Seo, H. Takeuchi, and Y. Shin, Ob- servation of wall-vortex composite defects in a spinor Bose-Einstein condensate, Phys. Rev. Lett. 122, 095301 (2019)

work page 2019