Pith. sign in

REVIEW 2 major objections 5 minor 4 cited by

Oscillons and bubbles in $Q$-ball dynamics

T0 review · 2 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Collisions of a Q-ball with its antiparticle become chaotic in the thin-wall regime, driven by internal modes and by short-lived bubbles of false vacuum that Goldstone waves can temporarily hold open.

desk verdict Solid Q-ball collision study with a genuinely new bubble-stabilization mechanism, but the 'chaos' claim needs numerical backstop before it should stand. read the letter →

arxiv 2509.03192 v1 pith:NQLNLCGJ submitted 2025-09-03 hep-th nlin.PS

D. Canillas Martínez , P. Dorey , T. Romańczukiewicz , P. M. Saffin , K. S{l}awińska , A. Wereszczyński This is my paper
classification hep-thnlin.PS
keywords Q-ballsnontopologicalsolitonssolitoncollisionsfalsevacuumGoldstonemodesoscillonsspectralwallschaos
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 sets out to show that Q-ball–anti-Q-ball collisions in the complex phi^6 model are chaotic in the thin-wall regime, and to identify the mechanism. Thin-wall Q-balls carry pronounced internal vibrational modes that support resonant energy transfer, and the collisions create ephemeral intermediate states — charged oscillons and, most notably, a bubble of false broken vacuum — that govern annihilation. The bubble, normally doomed to collapse under surface pressure, can be temporarily stabilized because the charge released by the colliding Q-balls excites massless Goldstone modes in the broken vacuum; these waves press on the bubble boundaries or become trapped as standing modes, and trapped modes can trigger spectral walls at critical bubble sizes. If the picture holds, Q-ball collisions are far richer than a simple kink-antikink analogy suggests, with direct consequences for how colliding Q-balls redistribute charge and energy in cosmological settings.

What carries the argument

The central object is the complex phi^6 model with potential V = |phi|^2 - |phi|^4 + beta|phi|^6, which for 1/4 <= beta < 1/3 possesses a false vacuum and therefore supports a bubble solution: a kink-antikink pair enclosing the false vacuum inside the true vacuum. In the thin-wall limit a Q-ball is itself a Q-kink–Q-antikink bound state whose surface structure makes it natural for collisions to transiently form such a bubble. The load-bearing mechanism is the massless Goldstone mode associated with the spontaneously broken vacuum inside the bubble: at linear order it decouples from the massive amplitude mode, and when excited by the charge released in a collision it either pushes on the bubb

What would settle it

Take one collision inside a chaotic window, rerun it on successively finer grids and with smaller time steps, and compare the final states; then compute finite-time Lyapunov exponents from nearby initial conditions. If the self-similar windows disappear under refinement or the exponents do not stay positive, the chaos claim loses its support.

Watch

Extended reading notes

Core claim

The central claim is that, in the thin-wall regime, Q-ball–anti-Q-ball collisions reveal chaotic behaviour, and this chaos has two complementary sources. The first is the standard resonant energy transfer mechanism: thin-wall Q-balls host well-pronounced internal modes that can temporarily absorb kinetic energy during a collision. The second, more distinctive source is the family of ephemeral states, especially the bubble of false broken vacuum, which acts as an intermediate state in QQ* annihilation. The bubble is usually short-lived, but when the Q-balls' charge delocalizes into the bubble it excites massless Goldstone modes of the broken vacuum. Those modes either exert radiation pressure

Load-bearing premise

The claim of chaos rests on the assumption that the extreme sensitivity to initial conditions and the self-similar patterns seen in the numerical simulations are genuine dynamics rather than artifacts of the integration scheme.

Editorial extensions

If this is right

  • Thin-wall QQ* collisions with a false vacuum produce a wide variety of final states — backscattered Q-balls, several emitted polarized Q-balls, oscillons, and charge-swapping states — selected chaotically by the initial velocity and relative phase.
  • Because the bubble stores U(1) charge as delocalized Goldstone waves, its collapse can re-confine the charge into Q-balls or oscillons, sometimes with the opposite sign to the incoming Q-ball, a charge transmutation seen in Q-ball–bubble collisions.
  • Trapped Goldstone modes generate spectral walls at specific bubble sizes, so a fine-tuned excitation can hold the bubble at a fixed size for a long time before it collapses or crosses the wall.
  • In the thick-wall regime, where Q-balls are weakly bound and lack pronounced internal modes, the same collisions reduce to simple backscattering or passing through, with almost no annihilation.
  • If Q-balls form from fragmentation of a scalar condensate, subsequent collisions will pass through these ephemeral states; the chaotic final-state selection described here could redistribute charge and energy among the surviving Q-balls and thereby affect their viability as dark matter.

Reading between the lines

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

  • The Goldstone-stabilization mechanism should extend to spherical bubbles in higher dimensions, where a closed wall can confine more standing waves and may make temporary bubble stabilization even longer-lived; the paper only demonstrates the effect in 1+1 dimensions.
  • The paper's chaos claim is open to a quantitative check: high-resolution runs with Lyapunov-exponent diagnostics would tell whether the self-similar windows are true resonance structure rather than numerical sensitivity.
  • Because the U(1) charge is continuous, bubbles can emit fractionally charged Q-balls; in models with quantized topological charge such fractional emission is forbidden, so bubble-mediated charge release could serve as a signature distinguishing global from topological charges.
  • The size-dependent trapped-mode spectrum suggests that other cavity-like bag configurations, such as oscillon bags in gapless models, should exhibit analogous spectral walls, connecting this bubble dynamics to a broader class of long-lived states.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript studies QQ* collisions in the complex ϕ6 model in 1+1 dimensions. It identifies three classes of non-perturbative states—charged/real oscillons (polarized Q-balls), false-vacuum bubbles, and Q-sphalerons—and argues that these ephemeral states, together with bound modes, control collision outcomes. The main claims are: (i) in the thin-wall regime, QQ* collisions exhibit chaotic, self-similar patterns in the final-state formation, driven by resonant energy transfer through internal modes; (ii) in the presence of a false vacuum, the intermediate bubble is key, and it can be temporarily stabilized by excited massless Goldstone modes; (iii) trapped Goldstone modes can produce spectral walls that arrest bubble collapse; (iv) Q-ball–bubble collisions show charge delocalization and emission of Q-balls with reversed charge. The paper combines analytical constructions (exact Q-ball profile, effective Lagrangian for the bubble mode) with extensive numerical scans over velocity, internal frequency and phase.

Significance. If the central claims hold, this is a substantial step toward understanding nontopological-soliton collisions: it connects QQ* scattering to the resonance structure known for kinks and vortices, and it identifies a new stabilization mechanism (Goldstone radiation pressure and trapped Goldstone modes) for false-vacuum bubbles. The effective Lagrangian for trapped modes and the spectral-wall prediction are valuable and falsifiable. However, the manuscript's headline claim of chaotic behaviour rests on numerical evidence that is not documented to the standard needed to exclude lattice artifacts. The paper does not provide convergence tests, a description of the integration scheme, or quantitative chaos diagnostics. The qualitative mechanisms themselves may survive such tests, but the current evidence is insufficient for the abstract's unqualified statement. For these reasons the contribution is potentially significant but needs a major revision.

major comments (2)
  1. [§6.3, Figs. 11, 15, 16; also Eq. (6.1)] The central claim that QQ* collisions in the thin-wall regime 'reveal chaotic behaviour' is based entirely on visual self-similarity and extreme sensitivity to v and δ in two-dimensional colour maps. No numerical scheme, grid spacing, time step, domain size, boundary conditions or energy-conservation error is reported. Integration times up to t=500 (Fig. 16) are long enough for emitted radiation to reach and reflect from the boundaries of a finite 1+1D box unless absorbing conditions are used, and reflected radiation is known to produce spurious bounce windows and artificial sensitivity in soliton-scattering simulations. Please provide the numerical details and, for representative parameter values, convergence tests under grid refinement, domain enlargement and (if not already used) absorbing/outgoing boundary conditions. In addition, a quantitative diagnostic of chaos—e.g., finite-time
  2. [§5.3, Eq. (5.15)–(5.20), Fig. 10] The spectral-wall mechanism is one of the paper's main explanatory tools for bubble stabilization, and the effective Lagrangian leading to a mode-induced repulsive force is a nice analytic result. However, its validation is only qualitative: a single trajectory (Fig. 10) is said to pause at the third spectral-wall position a_sw^(3)=3.5714, but no quantitative comparison is made between the full field-theory evolution and the adiabatic prediction—neither the resting radius versus time, nor the decay of the mode amplitude, nor the total time spent near the wall. Since the paper claims that the 'position agrees very well' with the critical value, please provide a quantitative comparison, including the effect of radiation/amplitude loss on the adiabatic invariant C in Eq. (5.18).
minor comments (5)
  1. [§6.3] The conclusion that 'a tiny change in the initial data can lead to a drastic change' is based on finite-time simulations; even if not genuine chaos, this is an interesting observation. I suggest softening the language (e.g., 'apparent chaos' or 'extreme sensitivity') until the numerical diagnostics are supplied.
  2. [§5.2, Fig. 8] The example of bubble stabilization uses a perturbation −i exp(−(x/8)^2)sin(0.4t), which adds net U(1) charge. The text notes this, but then states that zero-total-charge Goldstone modes can also stabilize the bubble. An explicit zero-charge example (or a sentence identifying one in the collision scans) would make the mechanism more convincing.
  3. [§6.4, Figs. 20–21] The sphaleron-mediated scenario is documented for a single parameter point (β=0.2501, ω0=0.02, v=0.3815). A brief statement of how generic this channel is (e.g., a small scan in v for this β) would help assess its role.
  4. [§2, Fig. 3] The vertical white dashed lines are described as 'the mass threshold', but the panels show two thresholds (ω=ω0±1?) and the caption is terse. Please clarify which dispersion branches are being plotted and how the power spectrum is normalized.
  5. [Eq. (6.1)] The initial data is a superposition of boosted Q-balls; it would be useful to state the initial separation 2x0 and how far it exceeds the Q-ball width, since the independence of the two incoming solitons is assumed.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: central claims rest on direct numerical evolution rather than on fitted parameters or self-citations.

full rationale

The paper's central claims are that thin-wall QQ* collisions exhibit chaotic, self-similar patterns, and that false-vacuum bubbles appear as intermediate states and can be temporarily stabilized by Goldstone modes. Both claims are tested by direct numerical evolution of the complex phi^6 field equations, not by fitting a parameter to a labeled prediction. The spectral modes of Q-balls are computed in-house (Sec. 2, Figs. 3-4), the bubble's linear perturbations and Goldstone/amplitude potentials are derived from the bubble profile (Sec. 5.2), and the spectral-wall positions are computed from the bubble's spectral problem and then compared with the numerical evolution (Sec. 5.3, Fig. 10), so the comparison is an independent test rather than a fit. The effective Lagrangian (5.15)-(5.20) is a collective-coordinate model obtained from the bubble ansatz and mode frequencies, not tuned to reproduce the QQ* collision outcome maps. The many self-citations ([21], [34], [35], [40], [41], etc.) supply terminology and previously observed mechanisms, but the load-bearing evidence for the present paper's claims is in its own simulations and spectral computations. The central 'chaotic behaviour' assertion is inferred from visual self-similarity and extreme sensitivity to initial conditions in the numerical scans; the lack of Lyapunov exponents and convergence checks is a legitimate robustness/correctness concern, but it is not circularity under the hard-rule test. No equation is shown to be equivalent to its own input by construction, and no fitted quantity is renamed as a prediction. Therefore the circularity score is low, reflecting only the pervasive but non-load-bearing use of prior work by the same authors.

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

The analysis introduces no free parameters fitted to data; beta, omega0, v, and delta are scanned as initial conditions. The main load-bearing inputs are the model choice and the numerical solver's accuracy, plus prior results from the same group (e.g., spectral walls, polarized Q-balls) that are treated as established.

assumptions (4)
  • standard math The field equations (2.5) and the Q-ball solutions (2.9) are correctly derived from the Lagrangian (2.1).
    The paper's analysis assumes these standard results.
  • domain assumption The chosen parameter values (beta=0.26, 0.5, 0.2501) are representative of the regimes claimed (thick-wall, thin-wall with and without false vacuum).
    Conclusions are drawn from these specific values, with no parameter sweeps for beta.
  • domain assumption The numerical solutions accurately represent the continuum dynamics; no discretization details or convergence tests are provided.
    The paper relies on the accuracy of its simulations without reporting numerical method details.
  • standard math Prior results on spectral walls (ref. [41]), oscillons (refs. [34,35]), and Q-ball perturbation theory (ref. [12]) are accepted as correct.
    The analysis builds on these established results.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Oscillons and bubbles in $Q$-ball dynamics." pith.science (2026). https://pith.science/paper/NQLNLCGJ

@misc{pith2026250903192,
  author       = {Pith},
  title        = {Pith review of: Oscillons and bubbles in $Q$-ball dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NQLNLCGJ}},
  note         = {Machine review of arXiv:2509.03192}
}
abstract

We show that, in the thin-wall regime, $Q$-ball--anti-$Q$-ball collisions reveal chaotic behaviour. This is explained by the resonant energy transfer mechanism triggered by the internal modes hosted by the $Q$-balls and by the existence of {\it ephemeral} states, that is unstable, sometimes even short-lived, field configurations that appear as intermediate states. The most important examples of such states are the {\it bubble} of the false broken vacuum, which as intermediate states govern the $QQ^*$ annihilation, and the {\it charged oscillons}. The usually short-lived bubble can be dynamically temporarily stabilized, which explains their importance in the dynamics of $Q$-balls. This happens due to the excitation of massless Goldstone modes, which, exerting pressure on the bubble boundaries or being trapped as bound modes, prevent the bubble from collapsing.

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Resonance phenomena in vortex-antivortex collisions

    hep-th 2025-10 conditional novelty 7.0 of 10

    Vortex–antivortex collisions in the deep type-II Abelian-Higgs model show multi-bounce windows embedded in annihilation regions, driven by a Feshbach resonant mode.

  2. Unified theory of oscillons and modes

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Oscillons are reinterpreted as localized resonant modes from threshold or antibound modes via nonlinearity, with wobblerons as new kink-oscillon bound states.

  3. Quantum-Corrected Q-balls in the Friedberg-Lee-Sirlin Model

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    Hartree quantum fluctuations in 3+1D simulations of the Friedberg-Lee-Sirlin model produce a regime where fluctuations carry significant Noether charge, periodic charge exchange occurs, and some classically stable Q-b...

  4. Preheating and oscillon formation in Einstein-scalar-Gauss-Bonnet gravity

    gr-qc 2026-07 unverdicted novelty 5.0 of 10

    Simulations in Einstein-scalar-Gauss-Bonnet gravity show oscillons form with similar properties to standard cases but trigger EFT breakdown for large couplings via high local curvatures.

Reference graph

Works this paper leans on

71 extracted references · 34 canonical work pages · cited by 4 Pith papers

  1. [1]

    Friedberg, T

    R. Friedberg, T. D. Lee and A. Sirlin, A Class of Scalar-Field Soliton Solutions in Three Space Dimensions, Phys. Rev. D 13 (1976) 2739–2761

    work page 1976

  2. [2]

    S. R. Coleman, Q-balls, Nucl. Phys. B 262 (1985) 263

    1985

  3. [3]

    Kusenko and M

    A. Kusenko and M. E. Shaposhnikov, Supersymmetric Q balls as dark matter , Phys. Lett. B 418 (1998) 46–54, [ hep-ph/9709492]. – 28 –

    arXiv 1998

  4. [4]

    Dine and A

    M. Dine and A. Kusenko, The Origin of the matter - antimatter asymmetry , Rev. Mod. Phys. 76 (2003) 1, [ hep-ph/0303065]

    arXiv 2003

  5. [5]

    Enqvist and A

    K. Enqvist and A. Mazumdar, Cosmological consequences of MSSM flat directions , Phys. Rept. 380 (2003) 99–234, [ hep-ph/0209244]

    arXiv 2003

  6. [6]

    Cardoso and P

    V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report , Living Rev. Rel. 22 (2019) 4, [ 1904.05363]

    arXiv 2019

  7. [7]

    Kusenko and A

    A. Kusenko and A. Mazumdar, Gravitational waves from fragmentation of a primordial scalar condensate into Q-balls , Phys. Rev. Lett. 101 (2008) 211301, [ 0807.4554]

    arXiv 2008

  8. [8]

    S. L. Liebling and C. Palenzuela, Dynamical boson stars , Living Rev. Rel. 26 (2023) 1, [1202.5809]

    arXiv 2023

Show all 71 references
  1. [9]

    J. C. Mourelle, N. Sanchis-Gual and J. A. Font, Close-knit relatives: reproducing galactic rotation curves with a two-component bosonic dark matter model , 2505.07465

  2. [10]

    T. D. Lee and Y. Pang, Nontopological solitons, Phys. Rept. 221 (1992) 251–350

    1992

  3. [11]

    Multamaki and I

    T. Multamaki and I. Vilja, Analytical and numerical properties of Q balls , Nucl. Phys. B 574 (2000) 130–152, [ hep-ph/9908446]

    2000 arXiv

  4. [12]

    Ciurla, P

    D. Ciurla, P. Dorey, T. Roma´ nczukiewicz and Y. Shnir, Perturbations of Q-balls: from spectral structure to radiation pressure, JHEP 07 (2024) 196, [ 2405.06591]

    2024 arXiv

  5. [13]

    Battye and P

    R. Battye and P. Sutcliffe, Q-ball dynamics , Nucl. Phys. B 590 (2000) 329–363, [hep-th/0003252]

    2000 arXiv

  6. [14]

    Axenides, S

    M. Axenides, S. Komineas, L. Perivolaropoulos and M. Floratos, Dynamics of nontopological solitons: Q balls , Phys. Rev. D 61 (2000) 085006, [ hep-ph/9910388]

    2000 arXiv

  7. [15]

    Multamaki and I

    T. Multamaki and I. Vilja, Q Ball collisions in the MSSM: Gravity mediated supersymmetry breaking, Phys. Lett. B 482 (2000) 161–166, [ hep-ph/0003270]

    2000 arXiv

  8. [16]

    Multamaki and I

    T. Multamaki and I. Vilja, Q ball collisions in the MSSM: Gauge mediated supersymmetry breaking, Phys. Lett. B 484 (2000) 283–288, [ hep-ph/0005162]

    2000 arXiv

  9. [17]

    Bowcock, D

    P. Bowcock, D. Foster and P. Sutcliffe, Q-balls, Integrability and Duality , J. Phys. A 42 (2009) 085403, [ 0809.3895]

    2009 arXiv

  10. [18]

    E. J. Copeland, P. M. Saffin and S.-Y. Zhou, Charge-Swapping Q-balls, Phys. Rev. Lett. 113 (2014) 231603, [ 1409.3232]

    2014 arXiv

  11. [19]

    P. M. Saffin, Q.-X. Xie and S.-Y. Zhou, Q-ball superradiance, Phys. Rev. Lett. 131 (Sep,

  12. [20]

    Cardoso, R

    V. Cardoso, R. Vicente and Z. Zhong, Energy Extraction from Q-balls and Other Fundamental Solitons, Phys. Rev. Lett. 131 (2023) 111602, [ 2307.13734]

    2023 arXiv

  13. [21]

    Alonso-Izquierdo, D

    A. Alonso-Izquierdo, D. C. Mart ´ ınez, T. Roma´ nczukiewicz, K. S lawi´ nska and A. Wereszczy´ nski,Excited oscillons and charge-swapping , 2504.17382

    arXiv

  14. [22]

    D. K. Campbell, J. F. Schonfeld and C. A. Wingate, Resonance structure in kink-antikink interactions in φ4 theory , Physica D 9 (1983) 1

    1983

  15. [23]

    Sugiyama, Kink-antikink collisions in the two-dimensional ϕ4 model, Prog

    T. Sugiyama, Kink-antikink collisions in the two-dimensional ϕ4 model, Prog. Theor. Phys. 61 (1979) 1550–1563

    1979

  16. [24]

    I. L. Bogolyubsky and V. G. Makhankov, On the Pulsed Soliton Lifetime in Two Classical Relativistic Theory Models, JETP Lett. 24 (1976) 12. – 29 –

    1976

  17. [25]

    Gleiser, Pseudostable bubbles , Phys

    M. Gleiser, Pseudostable bubbles , Phys. Rev. D 49 (1994) 2978–2981, [ hep-ph/9308279]

    1994 arXiv

  18. [26]

    E. J. Copeland, M. Gleiser and H. R. Muller, Oscillons: Resonant configurations during bubble collapse , Phys. Rev. D 52 (1995) 1920–1933, [ hep-ph/9503217]

    1995 arXiv

  19. [27]

    Graham and N

    N. Graham and N. Stamatopoulos, Unnatural Oscillon Lifetimes in an Expanding Background, Phys. Lett. B 639 (2006) 541–545, [ hep-th/0604134]

    2006 arXiv

  20. [28]

    Salmi and M

    P. Salmi and M. Hindmarsh, Radiation and Relaxation of Oscillons , Phys. Rev. D 85 (2012) 085033, [1201.1934]

    2012 arXiv

  21. [29]

    Fodor, P

    G. Fodor, P. Forgacs, Z. Horvath and M. Mezei, Computation of the radiation amplitude of oscillons, Phys. Rev. D 79 (2009) 065002, [ 0812.1919]

    2009 arXiv

  22. [30]

    Fodor, P

    G. Fodor, P. Forgacs, Z. Horvath and M. Mezei, Radiation of scalar oscillons in 2 and 3 dimensions, Phys. Lett. B 674 (2009) 319–324, [ 0903.0953]

    2009 arXiv

  23. [31]

    Zhang, M

    H.-Y. Zhang, M. A. Amin, E. J. Copeland, P. M. Saffin and K. D. Lozanov, Classical Decay Rates of Oscillons , JCAP 07 (2020) 055, [ 2004.01202]

    2020 arXiv

  24. [32]

    J. Olle, O. Pujolas and F. Rompineve, Recipes for oscillon longevity , JCAP 09 (2021) 015, [2012.13409]

    2021 arXiv

  25. [33]

    van Dissel, O

    F. van Dissel, O. Pujolas and E. I. Sfakianakis, Oscillon spectroscopy, JHEP 07 (2023) 194, [2303.16072]

    2023 arXiv

  26. [34]

    Blaschke, T

    F. Blaschke, T. Romanczukiewicz, K. Slawinska and A. Wereszczynski, Q-ball polarization - A smooth path to oscillons , Phys. Lett. B 865 (2025) 139468, [ 2502.20519]

    2025 arXiv

  27. [35]

    Blaschke, T

    F. Blaschke, T. Roma´ nczukiewicz, K. S lawi´ nska and A. Wereszczy´ nski,Oscillons from Q-Balls through Renormalization , Phys. Rev. Lett. 134 (2025) 081601, [ 2410.24109]

    2025 arXiv

  28. [36]

    Alonso-Izquierdo, D

    A. Alonso-Izquierdo, D. Canillas Mart ´ ınez, C. Garz´ on S´ anchez and M. Gonz´ alez Le´ on, Geometric construction of non-linear sigma models with q-ball/q-kink solutions , Chaos, Solitons & Fractals 181 (2024) 114732

    2024

  29. [37]

    Nugaev, A

    E. Nugaev, A. Shkerin and M. Smolyakov, Q-holes, JHEP 12 (2016) 032, [ 1609.05568]

    2016 arXiv

  30. [38]

    Kawasaki, K

    M. Kawasaki, K. Murai and F. Takahashi, Q-balls Under Spontaneously Broken U(1) Symmetry, 2504.13509

    arXiv

  31. [39]

    Kobayashi, K

    J. Kobayashi, K. Nakayama and M. Yamada, Decay rate of PQ-ball , 2504.13510

    arXiv

  32. [40]

    Alonso Izquierdo, N

    A. Alonso Izquierdo, N. S. Manton, J. Mateos Guilarte and A. Wereszczynski, Collective coordinate models for 2-vortex shape mode dynamics , Phys. Rev. D 110 (2024) 085006, [2405.20249]

    2024 arXiv

  33. [41]

    C. Adam, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Spectral Walls in Soliton Collisions, Phys. Rev. Lett. 122 (2019) 241601, [ 1903.12100]

    2019 arXiv

  34. [42]

    N. S. Manton, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Collective Coordinate Model of Kink-Antikink Collisions in ϕ4 Theory, Phys. Rev. Lett. 127 (2021) 071601, [2106.05153]

    2021 arXiv

  35. [43]

    Krusch, M

    S. Krusch, M. Rees and T. Winyard, Scattering of vortices with excited normal modes , Phys. Rev. D 110 (2024) 056050, [ 2406.04164]

    2024 arXiv

  36. [44]

    Bachmaier and A

    M. Bachmaier and A. Wereszczynski, Vortex anti-Vortex collisions. Work in progress

  37. [45]

    Dorey, A

    P. Dorey, A. Gorina, T. Roma´ nczukiewicz and Y. Shnir, Collisions of weakly-bound kinks in the Christ-Lee model, JHEP 09 (2023) 045, [ 2304.11710]. – 30 –

    2023 arXiv

  38. [46]

    Dorey, K

    P. Dorey, K. Mersh, T. Romanczukiewicz and Y. Shnir, Kink-antikink collisions in the ϕ6 model, Phys. Rev. Lett. 107 (2011) 091602, [ 1101.5951]

    2011 arXiv

  39. [47]

    Blaschke, T

    F. Blaschke, T. Roma´ nczukiewicz, K. S lawi´ nska and A. Wereszczy´ nski,Amplitude modulations and resonant decay of excited oscillons , Phys. Rev. E 110 (2024) 014203, [2403.00443]

    2024 arXiv

  40. [48]

    Navarro-Obreg´ on and J

    S. Navarro-Obreg´ on and J. Queiruga,Impact of the internal modes on the sphaleron decay , Eur. Phys. J. C 84 (2024) 821, [ 2406.05706]

    2024 arXiv

  41. [49]

    Navarro-Obreg´ on and J

    S. Navarro-Obreg´ on and J. M. Queiruga,Perturbed nonlinear dynamics and decay of sphalerons on circles , Physica D 481 (2025) 134805

    2025

  42. [50]

    Bachmaier, G

    M. Bachmaier, G. Dvali and J. S. Valbuena-Berm´ udez,Radiation emission during the erasure of magnetic monopoles , Phys. Rev. D 108 (2023) 103501, [ 2306.12958]

    2023 arXiv

  43. [51]

    Dvali and J

    G. Dvali and J. S. Valbuena-Berm´ udez,Erasure of strings and vortices , Phys. Rev. D 107 (2023) 035001, [ 2212.07535]

    2023 arXiv

  44. [52]

    Bachmaier, Private communication

    M. Bachmaier, Private communication

  45. [53]

    G. R. Dvali, H. Liu and T. Vachaspati, Sweeping away the monopole problem , Phys. Rev. Lett. 80 (1998) 2281–2284, [ hep-ph/9710301]

    1998 arXiv

  46. [54]

    Gleiser and J

    M. Gleiser and J. Thorarinson, A Phase transition in U(1) configuration space: Oscillons as remnants of vortex-antivortex annihilation , Phys. Rev. D 76 (2007) 041701, [hep-th/0701294]

    2007 arXiv

  47. [55]

    C. Adam, D. Ciurla, K. Oles, T. Romanczukiewicz and A. Wereszczynski, Sphalerons and resonance phenomenon in kink-antikink collisions , Phys. Rev. D 104 (2021) 105022, [2109.01834]

    2021 arXiv

  48. [56]

    van Dissel and O

    F. van Dissel and O. Pujol` as,Soft Oscillons , 2505.00890

    arXiv

  49. [57]

    Van Dissel and E

    F. Van Dissel and E. I. Sfakianakis, Symmetric multifield oscillons , Phys. Rev. D 106 (2022) 096018, [2010.07789]

    2022 arXiv

  50. [58]

    Shafi, E

    M. Shafi, E. J. Copeland, R. Mahbub, S. S. Mishra and S. Basak, Formation and decay of oscillons after inflation in the presence of an external coupling. Part I. Lattice simulations , JCAP 10 (2024) 082, [ 2406.00108]

    2024 arXiv

  51. [59]

    S. Li, M. Yamaguchi and Y.-l. Zhang, Decay and lifetime of oscillons coupled to an external scalar field: Insights from instability band analysis , 2507.13276

  52. [60]

    Alonso-Izquierdo and C

    A. Alonso-Izquierdo and C. G. Sanchez, Families of Q-balls in a deformed O(4) linear sigma model, Physica D: Nonlinear Phenomena 449 (2023) 133764, [ 2301.10739]

    2023 arXiv

  53. [61]

    Alonso-Izquierdo and C

    A. Alonso-Izquierdo and C. G. Sanchez, Defects composed of kinks and Q-balls: Analytical solutions and stability , Phys. Rev. D 107 (2023) 125004, [ 2303.01537]

    2023 arXiv

  54. [62]

    Alonso-Izquierdo, D

    A. Alonso-Izquierdo, D. C. Martinez, C. G. Sanchez, M. A. Gonzalez Leon and A. Wereszczynski, Stability and decay of composite kinks/Q-balls solutions in a deformed O(2N+1) linear sigma model , Chaos Solitons Fractals 188 (2024) 115489, [ 2407.13225]

    2024 arXiv

  55. [63]

    R. F. Dashen, B. Hasslacher and A. Neveu, Nonperturbative Methods and Extended Hadron Models in Field Theory 1. Semiclassical Functional Methods , Phys. Rev. D 10 (1974) 4114

    1974

  56. [64]

    Goldstone and R

    J. Goldstone and R. Jackiw, Quantization of Nonlinear Waves , Phys. Rev. D 11 (1975) 1486–1498. – 31 –

    1975

  57. [65]

    K. E. Cahill, A. Comtet and R. J. Glauber, Mass Formulas for Static Solitons , Phys. Lett. B 64 (1976) 283–285

    1976

  58. [66]

    L. D. Faddeev and V. E. Korepin, Quantum Theory of Solitons: Preliminary Version , Phys. Rept. 42 (1978) 1–87

    1978

  59. [67]

    Evslin, Manifestly Finite Derivation of the Quantum Kink Mass , JHEP 11 (2019) 161, [1908.06710]

    J. Evslin, Manifestly Finite Derivation of the Quantum Kink Mass , JHEP 11 (2019) 161, [1908.06710]

    2019 arXiv

  60. [68]

    Evslin and A

    J. Evslin and A. Garc ´ ıa Mart ´ ın-Caro,Spontaneous emission from excited quantum kinks , JHEP 12 (2022) 111, [ 2210.13791]

    2022 arXiv

  61. [69]

    Evslin, H

    J. Evslin, H. Liu and B. Zhang, Meson production from kink-meson scattering , Phys. Rev. D 107 (2023) 025012, [ 2211.01794]

    2023 arXiv

  62. [70]

    Evslin, Asymptotic states for kink–meson scattering , Eur

    J. Evslin, Asymptotic states for kink–meson scattering , Eur. Phys. J. C 83 (2023) 743, [2304.01564]

    2023 arXiv

  63. [71]

    Evslin, T

    J. Evslin, T. Roma´ nczukiewicz and A. Wereszczy´ nski,Quantum oscillons may be long-lived , JHEP 08 (2023) 182, [ 2305.18056]. – 32 –

    2023 arXiv

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.