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In a two-dimensional coherently coupled Bose superfluid, the rate of thermal false vacuum decay follows an exponential Arrhenius law, Γ = A e^(−βE_c), with the critical instanton energy E_c extracted from the magnetization dynamics.

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load-bearing objection 2D SGPE study of thermal false vacuum decay has a promising phase-dynamics result, but a common-noise prescription contradicts its own Eq. (4) and likely biases the extracted Arrhenius slopes. the 4 major comments →

arxiv 2602.03834 v2 pith:PYDPSKQ2 submitted 2026-02-03 cond-mat.quant-gas cond-mat.stat-mechhep-thquant-ph

Temperature driven false vacuum decay in coherently coupled Bose superfluids

Paniyanchatha Moolayil Sivasankar , Franco Dalfovo , Alessio Recati , Arko Roy This is my paper
classification cond-mat.quant-gas cond-mat.stat-mechhep-thquant-ph
keywords false vacuum decaystochastic Gross-Pitaevskii equationBose-Bose mixturethermal instantonmagnetization dynamicsrelative phase dynamicsnucleation rateultracold quantum gases
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.

False vacuum decay—the relaxation of a metastable state to a stable one—is a core problem in quantum field theory and cosmology, and this paper shows it can be emulated and quantified in a two-dimensional superfluid of two coherently coupled Bose gases. Using a stochastic Gross-Pitaevskii description, the authors prepare thermal false-vacuum states and track how the global magnetization decays as true-vacuum bubbles nucleate and grow. They find that the decay rate depends exponentially on inverse temperature, exactly the form predicted by finite-temperature instanton theory, and they extract the critical bubble energy for two barrier heights. They also discover that the relative phase between the two components is not locked during the decay but evolves, which affects the barrier-crossing dynamics. The result strengthens the case that ultracold atomic gases can serve as tabletop laboratories for field-theoretic processes like vacuum decay.

Core claim

The paper's central claim is that, in a two-dimensional coherently coupled Bose–Bose mixture, the rate Γ of thermal false vacuum decay is set by an exponential Arrhenius law Γ = A e^(−βE_c), with the critical energy E_c extracted from the exponential slope. The authors obtain E_c/k_B = (50±4) nK for detuning δ_f = −Ω and (63±6) nK for δ_f = −0.95Ω from the average-magnetization protocol, and (58±5) nK and (74±7) nK from the trajectory-counting protocol. They further claim that the relative phase φ of the two components, often assumed locked to cosφ = 1, actually evolves during the decay, and that this phase dynamics is needed to understand how the system crosses the energy barrier. The evide

What carries the argument

The central objects are the global magnetization Z(t) (the density imbalance between the two hyperfine components) and the relative phase φ(t) between them. The system is described by a Stochastic Gross-Pitaevskii equation (SGPE) that couples the low-energy c-fields to a thermal reservoir through dissipation γ and noise; initial false-vacuum states are equilibrated in a biased double-well landscape with detuning δ, then decay runs with γ = 0 under the projected Gross-Pitaevskii equation (PGPE). The decay rate Γ is extracted by exponential fitting of two survival estimators: the ensemble-averaged rescaled magnetization ⟨Z(t)⟩ and the fraction P(t) of trajectories still in the false vacuum. Th

Load-bearing premise

The decay is simulated with the dissipation and thermal noise switched off (γ = 0), so the system relies only on thermal fluctuations already present in the initial c-field state; if sustained coupling to the thermal reservoir is necessary for the correct thermally-activated rate, the extracted E_c values would be protocol-specific rather than universal.

What would settle it

A direct comparison to a full finite-temperature instanton computation of the critical bubble energy in 2D: the paper provides no analytical E_c, so if a Euclidean-action calculation for this complex scalar field yielded a value inconsistent with the fitted slopes (e.g., outside the 50–74 nK range), the interpretation would fail. Alternatively, repeating the decay with γ kept nonzero and observing a measurably different Γ or temperature dependence would falsify the claim that the γ = 0 protocol captures the same physics.

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

If this is right

  • If the exponential temperature dependence is correct, the decay rate in a 2D coherently coupled superfluid can be tuned by temperature, with the barrier height controlled by the final detuning δ_f.
  • The extracted critical energy E_c increases when the detuning is made more negative (higher barrier), consistent with the instanton picture.
  • Treatments that lock the relative phase to cosφ = 1 miss part of the barrier-crossing dynamics; a full complex-scalar description of the field is needed.
  • The SGPE/PGPE protocol, including the γ = 0 decay stage, is a viable numerical tool for predicting finite-temperature decay rates that can be compared with experiments.
  • Temperature-driven vacuum decay, not only quantum decay, is accessible in near-term ultracold atom experiments in two dimensions.
  • Both survival-probability protocols yield the same exponential temperature dependence, so the extracted E_c is robust to the choice of estimator within statistical uncertainty.

Where Pith is reading between the lines

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

  • A direct experimental test could measure the same Arrhenius slope in a homogeneous 2D mixture; if the extracted E_c differs from the simulation, the γ = 0 protocol would need to be revisited.
  • The observed phase dynamics hints that the critical bubble in this system is not a purely magnetization profile; a full Euclidean-action instanton calculation with both Z and φ structure would provide a sharper, parameter-free prediction for E_c.
  • The small difference between the two protocols' E_c values may reflect contributions from post-nucleation growth; separating nucleation from growth could refine the extracted barrier energy.
  • The same protocol could be extended to map how E_c scales with coupling strength and system size, providing a benchmark for finite-temperature instanton theory beyond one dimension.

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

4 major / 5 minor

Summary. The paper uses the Stochastic Gross-Pitaevskii equation (SGPE) to simulate temperature-driven false vacuum decay in a two-dimensional coherently coupled Bose-Bose mixture. Thermal equilibrium states are prepared at positive detuning, the detuning is ramped to negative values to create a false vacuum, and the decay dynamics is studied after switching off dissipation. Decay rates are extracted from the ensemble-averaged magnetization and from a trajectory-counting survival probability, and fitted to an Arrhenius form Γ=A exp(−βE_c), yielding critical energies E_c that increase with the final detuning. The paper also reports that the relative phase is not locked during decay and argues that phase dynamics is relevant for barrier crossing. The central claim is that the simulated rates show an exponential temperature dependence consistent with finite-temperature instanton theory.

Significance. If the technical concerns are resolved, this would be a useful extension of false-vacuum-decay simulations to two dimensions and would provide a concrete numerical demonstration that the relative phase can evolve during bubble nucleation, in contrast to the phase-locked assumption used in several earlier analyses. The paper is transparent about treating E_c and A as fitting parameters and about the finite system size, and it employs bootstrapping to estimate statistical errors. However, the current evidence is insufficient to claim quantitative verification of the thermal-instanton prediction: the Arrhenius slope is a fit output, the common-noise prescription suppresses stochastic driving of the spin channel, and the decay stage is simulated without reservoir coupling.

major comments (4)
  1. [Sec. II.B, Eq. (4)] Eq. (4) specifies ⟨η_i(x,t) η_j^*(x',t')⟩ ∝ δ_{ij}, i.e., independent noises for the two components. The text immediately says 'we assume that the noise term is the same for both components.' These two statements are mutually exclusive. With a common noise, the relative-phase/magnetization channel (ψ_1 − ψ_2) receives no stochastic force during thermalization, so the initial fluctuations that seed bubble nucleation are not sampled from the canonical distribution at temperature T. This directly affects the Arrhenius slope extracted in Fig. 5. The authors must clarify which noise prescription was used; if common noise was used, they should re-examine the spin-channel fluctuations, and if Eq. (4) was used, the implementation contradicts the text.
  2. [Sec. III, first paragraph] Setting γ=0 during the decay stage removes the coupling to the thermal reservoir, so Eq. (3) becomes a conservative projected Gross-Pitaevskii equation with no noise. Temperature then enters only through the initial condition at the end of the ramp; subsequent decay is the Hamiltonian relaxation of a stochastic initial state. This is not the sustained thermal activation assumed in Linde's instanton theory. The claim that this 'keeps the relevant effects of thermal fluctuations within the c-fields' needs explicit support. A comparison with γ≠0 during decay, or at least a test of the insensitivity of Γ to γ, is required before the extracted E_c can be identified with the thermal instanton energy.
  3. [Sec. III.B, Fig. 5] The two extraction protocols give E_c/k_B = 50±4 nK and 58±5 nK for δ_f = −Ω, and 63±6 nK and 74±7 nK for δ_f = −0.95Ω. These values differ by 15–20%, which is larger than the quoted error bars. The paper acknowledges that the rates are 'not identical' but does not discuss this systematic discrepancy. Because the central result is the slope E_c, the discrepancy must be reconciled or included in a systematic error budget, for example by studying the fit-window dependence and the post-nucleation contribution to ⟨Z(t)⟩.
  4. [Sec. III.B, Eq. (5)] The text explicitly states that for the 2D configuration E_c and A are treated as fitting parameters. The linearity of Fig. 5 therefore tests only whether the data can be parametrized by an Arrhenius form; it is not an independent verification of instanton theory. To make the claimed agreement quantitative, the paper should either compute E_c independently (for example from a critical-bubble/instanton solution of the 2D equations of motion) or soften the claim to 'consistent with a thermally activated exponential with a temperature-independent energy scale.'
minor comments (5)
  1. [Sec. II.C] The trajectory-selection threshold Z>0.2 is stated to be robust, but no quantitative evidence is shown. Please provide results for at least one alternative threshold (e.g., Z>0.1 or Z>0.3) to support this statement.
  2. [Sec. III.B] The fitting window ⟨Z(t)⟩ ∈ [0.5,0.9] is chosen ad hoc. The effect of changing this window on Γ and E_c should be reported, especially given the protocol discrepancy in Fig. 5.
  3. [Sec. III.C] The statement that 'the energy has its maximum within the same interval' is not supported by any figure or quantitative result. Either show the energy curve or remove the claim.
  4. [Sec. II.B] The notation T_s = |κ|n/k_B is introduced but the dimensionless temperature T/T_s is later used inconsistently (e.g., 'T = 5.5T_s' vs. 'T_s/T' in Fig. 5). Clarify the notation in the captions and text.
  5. [Title] The title 'Temperature driven' should be hyphenated as 'Temperature-driven'.

Circularity Check

1 steps flagged

Arrhenius form is fitted, not independently predicted; reported E_c values are fit outputs rather than theoretical predictions.

specific steps
  1. fitted input called prediction [Sec. III.B (Decay rate), Eq. (5), Fig. 5]
    "For our two-dimensional configuration there are no available results and in the following we treat them as fitting parameters. ... The resulting linear dependence is consistent with the predictions of the instanton theory, expressed by Eq. (5). The slope can therefore be identified as the critical instanton energy, E_c/k_B."

    Eq. (5) is introduced as the instanton prediction, but E_c and A are then declared fitting parameters and the decay-rate data are fitted with exactly this Arrhenius form. The subsequent statement that the data are 'consistent with the predictions of the instanton theory' therefore reports the quality of a fit, not a test of a prediction: the fitted slopes are renamed as 'critical instanton energy' E_c. No independent theoretical value of E_c for 2D is computed or compared, so the central quantitative claim (exponential T dependence and the reported E_c values) is a parametrization of the data rather than a derived prediction.

full rationale

The simulation study is largely self-contained: initial states are generated by SGPE, decay rates are extracted from survival probabilities, and the phase-dynamics observation is independent of the Arrhenius fit. The main circularity concern is limited to the presentation of the Arrhenius fit as 'agreement with instanton theory': since E_c and A are fitting parameters (stated explicitly), the linear Arrhenius plot is a fit-quality statement rather than a test of a numerical prediction. The reported E_c values are therefore fit outputs, not first-principles predictions. No load-bearing self-citation chains or imported uniqueness theorems were found; citations to the authors' prior work establish the model and SGPE framework but do not by themselves force the results. The common-noise assumption (η1=η2) and the γ=0 decay protocol are physical limitations that could bias E_c, but they are correctness risks, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central quantitative content (E_c) is a fit to the observed decay rates, not a derivation. The SGPE, noise form, and cutoff are imported from prior literature. No new entities are introduced. Several hand-chosen parameters (threshold, fit window) affect the results.

free parameters (4)
  • E_c (critical instanton energy, slope of ln Γ vs 1/T) = 50±4 nK (⟨Z⟩, δ_f=-Ω); 63±6 nK (⟨Z⟩, δ_f=-0.95Ω); 58±5, 74±7 nK (P protocol)
    Fitted to the simulated decay rates; no independent 2D analytical prediction is available.
  • Prefactor A (A_Z/A_P intercepts) = Not reported numerically
    Fitted per temperature and protocol in Eq. (5); only the slope E_c is interpreted physically.
  • Trajectory selection threshold Z>0.2 at t=0 = 0.2
    Hand-chosen to discard trajectories that decayed during the ramp; authors claim robustness, but this is a post-hoc selection.
  • Fit window for ⟨Z(t)⟩ ∈ [0.5,0.9] = 0.5–0.9
    Chosen to avoid early- and late-time effects; affects Γ and hence E_c.
axioms (5)
  • domain assumption SGPE with projector and Gaussian noise faithfully samples finite-temperature equilibrium and dynamics of the coherently coupled mixture
    Used to prepare false-vacuum states and to justify the noise correlation Eq. (4).
  • domain assumption Noise term is identical for both components
    Follows Refs. [47-49]; affects spin-channel fluctuations and therefore nucleation dynamics.
  • ad hoc to paper Setting γ=0 during decay leaves intrinsic FVD dynamics and does not require sustained reservoir noise
    Crucial for the simulation protocol; no quantitative justification of timescale separation is given.
  • domain assumption Instanton picture with Boltzmann-weighted critical bubble (Eq. 5) applies in 2D with E_c temperature-independent in the simulated range
    Used to interpret the linearity of Fig. 5; no 2D calculation of E_c is provided.
  • domain assumption Initial equilibration reaches a thermal state of the spin degrees of freedom
    Stabilization of atom number is used as the equilibration criterion; no direct check of the Gibbs distribution is shown.

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read the original abstract

The relaxation of a quantum field from a metastable state (false vacuum) to a stable one (true vacuum), also known as false vacuum decay, is a fundamental problem in quantum field theory and cosmology. We study this phenomenon using a two-dimensional interacting and coherently coupled Bose-Bose mixture, a platform that has already been employed experimentally to investigate false vacuum decay in one dimension. In such a mixture, it is possible to define an effective magnetization that acts as a quantum field variable. Using the Stochastic Gross-Pitaevskii equation (SGPE), we prepare thermal equilibrium states in the false vacuum and extract decay rates from the magnetization dynamics. The decay rates show an exponential dependence on temperature, in line with the thermal theory of instantons. Since the SGPE is based on complex scalar fields, it also allows us to explore the behavior of the phase, which turns out to become dynamic during decay. Our results confirm the SGPE as an effective tool for studying coupled magnetization and phase dynamics and the associated instanton physics in ultracold quantum gases.

Figures

Figures reproduced from arXiv: 2602.03834 by Alessio Recati, Arko Roy, Franco Dalfovo, Paniyanchatha Moolayil Sivasankar.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of false vacuum decay through [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Panels [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Logarithm of survival probability [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Magnetization and relative phase dynamics for three [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

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Reference graph

Works this paper leans on

64 extracted references · 6 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Coleman, Fate of the false vacuum: Semiclassical the- ory, Phys

    S. Coleman, Fate of the false vacuum: Semiclassical the- ory, Phys. Rev. D15, 2929 (1977)

    1977

  2. [2]

    C. G. Callan and S. Coleman, Fate of the false vacuum. ii. first quantum corrections, Phys. Rev. D16, 1762 (1977)

    1977

  3. [3]

    I. Y. Kobzarev, L. B. Okun, and M. B. Voloshin, Bubbles in metastable vacuum, Yad. Fiz.20, 1229 (1974)

    1974

  4. [4]

    Coleman and F

    S. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D21, 3305 (1980)

    1980

  5. [5]

    Hindmarsh, M

    M. Hindmarsh, M. L¨ uben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes , 24 (2021)

    2021

  6. [6]

    Burda, R

    P. Burda, R. Gregory, and I. G. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett.115, 071303 (2015)

    2015

  7. [7]

    Stone, Semiclassical methods for unstable states, Phys

    M. Stone, Semiclassical methods for unstable states, Phys. Lett. B67, 186 (1977)

    1977

  8. [8]

    M. E. Shaposhnikov, Baryon asymmetry of the universe in standard electroweak theory, Nucl. Phys. B287, 757 8 (1987)

    1987

  9. [9]

    A. J. Baldwin, T. P. J. Knowles, G. G. Tartaglia, A. W. Fitzpatrick, G. L. Devlin, S. L. Shammas, C. A. Waudby, M. F. Mossuto, S. Meehan, S. L. Gras, J. Christodoulou, S. J. Anthony-Cahill, P. D. Barker, M. Vendruscolo, and C. M. Dobson, Metastability of native proteins and the phenomenon of amyloid formation, J. Am. Chem. Soc. 133, 14160 (2011)

    2011

  10. [10]

    D. K. Ghosh and A. Ranjan, The metastable states of proteins, Protein Sci.29, 1559 (2020)

    2020

  11. [11]

    D. W. Oxtoby, Homogeneous nucleation: theory and ex- periment, J. Phys.: Condens. Matter4, 7627 (1992)

    1992

  12. [12]

    P. G. Debenedetti and F. H. Stillinger, Supercooled liq- uids and the glass transition, Nature410, 259 (2001)

    2001

  13. [13]

    Coldea, D

    R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzyn- ska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Quantum criticality in an Ising chain: Ex- perimental evidence for emergentE 8 symmetry, Science 327, 177 (2010)

    2010

  14. [14]

    S. B. Rutkevich, Decay of the metastable phase ind= 1 andd= 2 Ising models, Phys. Rev. B60, 14525 (1999)

    1999

  15. [15]

    Sinha, T

    A. Sinha, T. Chanda, and J. Dziarmaga, Nonadiabatic dynamics across a first-order quantum phase transition: Quantized bubble nucleation, Phys. Rev. B103, L220302 (2021)

    2021

  16. [16]

    Lagnese, F

    G. Lagnese, F. M. Surace, S. Morampudi, and F. Wilczek, Detecting a long-lived false vacuum with quantum quenches, Phys. Rev. Lett.133, 240402 (2024)

    2024

  17. [17]

    Johansen, A

    C. Johansen, A. Recati, I. Carusotto, and A. Biella, Many-body theory of false vacuum decay in quantum spin chains (2025), arXiv:2508.13780

    Pith/arXiv arXiv 2025

  18. [18]

    Paveˇ si´ c, M

    L. Paveˇ si´ c, M. Di Liberto, and S. Montangero, Scattering and induced false vacuum decay in the two-dimensional quantum Ising model (2025), arXiv:2509.02702

    arXiv 2025

  19. [19]

    Maertens, J

    D. Maertens, J. Haegeman, and K. Van Acoleyen, Real- time bubble nucleation and growth for false vacuum de- cay on the lattice (2025), arXiv:2508.13645

    Pith/arXiv arXiv 2025

  20. [20]

    Borla, A

    U. Borla, A. Lazarides, C. Groß, and J. C. Halimeh, Mi- croscopic Dynamics of False Vacuum Decay in the 2+1D Quantum Ising Model (2026), arXiv:2601.04305

    arXiv 2026

  21. [21]

    Abel and M

    S. Abel and M. Spannowsky, Quantum-field-theoretic simulation platform for observing the fate of the false vacuum, PRX Quantum2, 010349 (2021)

    2021

  22. [22]

    Vodeb, J.-Y

    J. Vodeb, J.-Y. Desaules, A. Hallam, A. Rava, G. Hu- mar, D. Willsch, F. Jin, M. Willsch, K. Michielsen, and Z. Papi´ c, Stirring the false vacuum via interacting quan- tized bubbles on a 5,564-qubit quantum annealer, Nat. Phys.21, 386 (2025)

    2025

  23. [23]

    Fialko, B

    O. Fialko, B. Opanchuk, A. I. Sidorov, P. D. Drummond, and J. Brand, The universe on a table top: Engineer- ing quantum decay of a relativistic scalar field from a metastable vacuum, J. Phys. B50, 024003 (2017)

    2017

  24. [24]

    Braden, M

    J. Braden, M. C. Johnson, H. V. Peiris, and S. Weinfurt- ner, Towards the cold atom analog false vacuum, J. High Energy Phys.07, 014

  25. [25]

    T. P. Billam, K. Brown, and I. G. Moss, Simulating cos- mological supercooling with a cold-atom system, Phys. Rev. A102, 043324 (2020)

    2020

  26. [26]

    T. P. Billam, K. Brown, A. J. Groszek, and I. G. Moss, Simulating cosmological supercooling with a cold atom system. ii. thermal damping and parametric instability, Phys. Rev. A104, 053309 (2021)

    2021

  27. [27]

    T. P. Billam, K. Brown, and I. G. Moss, False-vacuum decay in an ultracold spin-1 Bose gas, Phys. Rev. A105, L041301 (2022)

    2022

  28. [28]

    Zenesini, A

    A. Zenesini, A. Berti, R. Cominotti, C. Rogora, I. G. Moss, T. P. Billam, I. Carusotto, G. Lamporesi, A. Re- cati, and G. Ferrari, False vacuum decay via bubble for- mation in ferromagnetic superfluids, Nat. Phys.20, 558 (2024)

    2024

  29. [29]

    Darbha, M

    S. Darbha, M. Kornjaˇ ca, F. Liu, J. Balewski, M. R. Hirs- brunner, P. L. S. Lopes, S.-T. Wang, R. Van Beeumen, D. Camps, and K. Klymko, False vacuum decay and nu- cleation dynamics in neutral atom systems, Phys. Rev. B110, 155103 (2024)

    2024

  30. [30]

    Brown, I

    K. Brown, I. G. Moss, and T. P. Billam, Mitigating boundary effects in finite temperature simulations of false vacuum decay (2025), arXiv:2504.03509

    Pith/arXiv arXiv 2025

  31. [31]

    A. C. Jenkins, H. V. Peiris, and A. Pontzen, Bubbles in a box: Eliminating edge nucleation in cold-atom simulators of vacuum decay, Phys. Rev. A112, 023318 (2025)

    2025

  32. [32]

    Recati and S

    A. Recati and S. Stringari, Coherently coupled mixtures of ultracold atomic gases, Annu. Rev. Condens. Matter Phys.13, 407 (2022)

    2022

  33. [33]

    Cominotti, C

    R. Cominotti, C. Baroni, C. Rogora, D. Andreoni, G. Guarda, G. Lamporesi, G. Ferrari, and A. Zenesini, Observation of temperature effects on false vacuum decay in atomic quantum gases, Phys. Rev. Lett.135, 183401 (2025)

    2025

  34. [34]

    Zibold, E

    T. Zibold, E. Nicklas, C. Gross, and M. K. Oberthaler, Classical bifurcation at the transition from Rabi to Josephson dynamics, Phys. Rev. Lett.105, 204101 (2010)

    2010

  35. [35]

    Farolfi, A

    A. Farolfi, A. Zenesini, D. Trypogeorgos, C. Mordini, A. Gallem ´ ı, A. Roy, A. Recati, G. Lamporesi, and G. Fer- rari, Quantum-torque-induced breaking of magnetic in- terfaces in ultracold gases, Nat. Phys.17, 1359 (2021)

    2021

  36. [36]

    Farolfi, A

    A. Farolfi, A. Zenesini, R. Cominotti, D. Trypogeorgos, A. Recati, G. Lamporesi, and G. Ferrari, Manipulation of an elongated internal Josephson junction of bosonic atoms, Phys. Rev. A104, 023326 (2021)

    2021

  37. [37]

    Eto and M

    M. Eto and M. Nitta, Confinement of half-quantized vor- tices in coherently coupled Bose-Einstein condensates: Simulating quark confinement in a qcd-like theory, Phys. Rev. A97, 023613 (2018)

    2018

  38. [38]

    Cominotti, A

    R. Cominotti, A. Berti, C. Dulin, C. Rogora, G. Lam- poresi, I. Carusotto, A. Recati, A. Zenesini, and G. Fer- rari, Ferromagnetism in an extended coherently coupled atomic superfluid, Phys. Rev. X13, 021037 (2023)

    2023

  39. [39]

    A. D. Linde, Decay of the false vacuum at finite temper- ature, Nucl. Phys. B216, 421 (1983), [Erratum: Nucl. Phys. B 223, 544 (1983)]

    1983

  40. [40]

    H. T. C. Stoof and M. J. Bijlsma, Dynamics of fluctuating Bose–Einstein condensates, J. Low Temp. Phys.124, 431 (2001)

    2001

  41. [41]

    N. P. Proukakis and B. Jackson, Finite-temperature mod- els of Bose-Einstein condensation, J. Phys. B: At. Mol. Opt. Phys.41, 203002 (2008)

    2008

  42. [42]

    P. B. Blakie, A. S. Bradley, M. J. Davis, R. J. Ballagh, and C. W. Gardiner, Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques, Adv. Phys.57, 363 (2008)

    2008

  43. [43]

    A. Roy, M. Ota, F. Dalfovo, and A. Recati, Finite- temperature ferromagnetic transition in coherently cou- pled Bose gases, Phys. Rev. A107, 043301 (2023)

    2023

  44. [44]

    A. S. Bradley and P. B. Blakie, Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates, Phys. Rev. A90, 023631 (2014). 9

    2014

  45. [45]

    M. Ota, F. Larcher, F. Dalfovo, L. Pitaevskii, N. P. Proukakis, and S. Stringari, Collisionless sound in a uni- form two-dimensional Bose gas, Phys. Rev. Lett.121, 145302 (2018)

    2018

  46. [46]

    A. Roy, M. Ota, A. Recati, and F. Dalfovo, Finite- temperature spin dynamics of a two-dimensional Bose- Bose atomic mixture, Phys. Rev. Res.3, 013161 (2021)

    2021

  47. [47]

    C.-F. Liu, H. Fan, Y.-C. Zhang, D.-S. Wang, and W.- M. Liu, Circular-hyperbolic skyrmion in rotating pseudo- spin-1/2 Bose-Einstein condensates with spin-orbit cou- pling, Phys. Rev. A86, 053616 (2012)

    2012

  48. [48]

    Su, I.-K

    S.-W. Su, I.-K. Liu, Y.-C. Tsai, W. M. Liu, and S.- C. Gou, Crystallized half-skyrmions and inverted half- skyrmions in the condensation of spin-1 Bose gases with spin-orbit coupling, Phys. Rev. A86, 023601 (2012)

    2012

  49. [49]

    Su, I.-K

    S.-W. Su, I.-K. Liu, S.-C. Gou, R. Liao, O. Fialko, and J. Brand, Hidden long-range order in a spin-orbit- coupled two-dimensional Bose gas, Phys. Rev. A95, 053629 (2017)

    2017

  50. [50]

    Sakmann and M

    K. Sakmann and M. Kasevich, Single-shot simulations of dynamic quantum many-body systems, Nat. Phys.12, 451 (2016)

    2016

  51. [51]

    Sakmann and M

    K. Sakmann and M. Kasevich, Reply to the corre- spondence of Drummond and Brand [arxiv:1610.07633] (2017), arXiv:1702.01211

    Pith/arXiv arXiv 2017

  52. [52]

    Single-shot simula- tions of dynamic quantum many-body systems

    M. K. Olsen, J. F. Corney, R. J. Lewis-Swan, and A. S. Bradley, Correspondence on “Single-shot simula- tions of dynamic quantum many-body systems” (2017), arXiv:1702.00282

    Pith/arXiv arXiv 2017

  53. [53]

    A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose-Einstein condensation of atoms in a uniform potential, Phys. Rev. Lett.110, 200406 (2013)

    2013

  54. [54]

    J. L. Ville, R. Saint-Jalm, E. Le Cerf, M. Aidelsburger, S. Nascimb` ene, J. Dalibard, and J. Beugnon, Sound prop- agation in a uniform superfluid two-dimensional Bose gas, Phys. Rev. Lett.121, 145301 (2018)

    2018

  55. [55]

    Cominotti, A

    R. Cominotti, A. Berti, A. Farolfi, A. Zenesini, G. Lam- poresi, I. Carusotto, A. Recati, and G. Ferrari, Observa- tion of massless and massive collective excitations with Faraday patterns in a two-component superfluid, Phys. Rev. Lett.128, 210401 (2022)

    2022

  56. [56]

    Affleck, Quantum-statistical metastability, Phys

    I. Affleck, Quantum-statistical metastability, Phys. Rev. Lett.46, 388 (1981)

    1981

  57. [57]

    E. R. Garcia and J. Hofmann, Instanton theory and fluc- tuation corrections to the thermal nucleation rate of a ferromagnetic superfluid (2026), arXiv:2512.20734

    arXiv 2026

  58. [58]

    Prokof’ev, O

    N. Prokof’ev, O. Ruebenacker, and B. Svistunov, Critical point of a weakly interacting two-dimensional Bose gas, Phys. Rev. Lett.87, 270402 (2001)

    2001

  59. [59]

    Lagnese, F

    G. Lagnese, F. M. Surace, M. Kormos, and P. Calabrese, False vacuum decay in quantum spin chains, Phys. Rev. B104, L201106 (2021)

    2021

  60. [60]

    P ˆ ırvu, A

    D. P ˆ ırvu, A. Shkerin, and S. Sibiryakov, Thermal false vacuum decay in (1+1)-dimensions: Evidence for non- equilibrium dynamics (2024), arXiv:2408.06411

    Pith/arXiv arXiv 2024

  61. [61]

    T. P. Billam, R. Gregory, F. Michel, and I. G. Moss, Simulating seeded vacuum decay in a cold atom system, Phys. Rev. D100, 065016 (2019)

    2019

  62. [62]

    This prevents a direct access to the intrin- sic statistical distribution of Γ

    The decay rate, Γ is extracted from the survival prob- ability⟨Z(t)⟩, after averaging over individual stochastic realizations. This prevents a direct access to the intrin- sic statistical distribution of Γ. Bootstrapping provides a way to estimate the uncertainty of the intrinsic distribu- tion from the existing dataset (N= 100) without gen- erating addit...

  63. [63]

    Sz´ asz-Schagrin and G

    D. Sz´ asz-Schagrin and G. Tak´ acs, False vacuum decay in the (1+1)-dimensionalφ 4 theory, Phys. Rev. D106, 025008 (2022)

    2022

  64. [64]

    Berera, J

    A. Berera, J. Mabillard, B. W. Mintz, and R. O. Ramos, Formulating the Kramers problem in field theory, Phys. Rev. D100, 076005 (2019)

    2019