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arxiv: 2605.12633 · v1 · submitted 2026-05-12 · ✦ hep-th · nlin.PS

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Collision Dynamics of False-Vacuum Oscillons

J. G. F. Campos , N. S. Manton , Azadeh Mohammadi
Authors on Pith no claims yet

Pith reviewed 2026-05-14 20:10 UTC · model grok-4.3

classification ✦ hep-th nlin.PS
keywords oscillonsfalse vacuumsphaleronkink-antikinkphase transitionscalar fieldsresonancescollision dynamics
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The pith

Oscillon collisions in false-vacuum scalar theories can trigger phase transitions to the true vacuum by forming kink-antikink pairs.

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

The paper examines how oscillons collide in scalar field models with metastable false vacua. It uses a small-amplitude expansion to build the oscillon profiles and then simulates pairwise collisions numerically. The results show phase-dependent forces, resonant scattering, and in one class of potentials, the possibility that collisions supply enough energy to cross the sphaleron and create kink-antikink pairs that drive the vacuum decay. A sympathetic reader would care because this identifies a classical, collision-mediated route to phase transitions that might operate alongside quantum tunneling.

Core claim

In the normal class of potentials, when two oscillons collide with sufficient total energy, the field configuration can surmount the sphaleron barrier and evolve into a kink-antikink pair, thereby initiating the transition from the false vacuum to the true vacuum.

What carries the argument

The sphaleron barrier in the normal potential, which colliding oscillons must overcome to produce true-vacuum kink-antikink pairs.

Load-bearing premise

The small-amplitude Fodor expansion yields oscillon shapes whose high-energy collision behavior remains qualitatively correct even when the energy suffices to cross the sphaleron barrier.

What would settle it

A simulation in which the total energy of colliding oscillons exceeds the sphaleron energy yet no kink-antikink pair forms, or the opposite outcome below that threshold.

Figures

Figures reproduced from arXiv: 2605.12633 by Azadeh Mohammadi, J. G. F. Campos, N. S. Manton.

Figure 1
Figure 1. Figure 1: Potential in the normal model as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Sphaleron profiles ϕS(x) for several values of s. up to the third order, where p1(ζ) = r 2 λ sech(ζ), (II.13) p3(ζ) = 280g 4 2 − 132g 2 2λ + 9λ 2 81√ 2 λ5/2 sech(ζ) − [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Stability potential V ′′(ϕS(x; s)) as function of x. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 s ω 2 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Small oscillation spectrum around the sphaleron [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Potential in the inverted model as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Sphaleron profiles ψS,+(x) for several values of r. The inverted model also admits two distinct sphalerons, ψS,+(x; r) = − i 2 h tanh x/2 + ir − tanh x/2 − ir i = sin(2r) cosh(x) + cos(2r) , (III.8) ψS,−(x; r) = − i 2 h coth x/2 + ir − coth x/2 − ir i = − sin(2r) cosh(x) − cos(2r) , (III.9) related by ψS,− [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Stability potential U ′′(ψS,+; r) as function of x. 0 π 8 π 4 3 π 8 π 2 -8.0 -6.0 -4.0 -2.0 0.0 0 π 8 π 4 3 π 8 π 2 -8.0 -6.0 -4.0 -2.0 0.0 r ω 2 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Small oscillation spectrum around the sphaleron [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Time evolution of the field at the center of Fodor oscillons and a kicked sphaleron. [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Power spectra of Fodor oscillons and a kicked sphaleron, as functions of [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Power spectrum of a kicked sphaleron as function of [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Spacetime field evolution in symmetric, normal-model oscillon collisions: (a) [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Spacetime field evolution in normal-model oscillon collisions for [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Spacetime evolution of the field in inverted-model oscillon collisions: (a) Reflection, [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Field at the center of a normal-model oscillon collision, as function of time [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Snapshots of a collision between two oscillons. The field passes over the sphaleron [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Twice the oscillon mass, as function of amplitude [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Field at the center of an inverted-model oscillon collision. [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Field at the center of a normal-model oscillon collision, for varying phase [PITH_FULL_IMAGE:figures/full_fig_p019_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Field at the center of an asymmetric oscillon collision. (a) We fix [PITH_FULL_IMAGE:figures/full_fig_p020_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Field at the center of a collision between kicked sphalerons. [PITH_FULL_IMAGE:figures/full_fig_p020_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Separation windows and time before the first bounce. The slope gives a resonant [PITH_FULL_IMAGE:figures/full_fig_p021_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Field at the center of oscillon collisions in two narrow intervals of velocity [PITH_FULL_IMAGE:figures/full_fig_p022_23.png] view at source ↗
read the original abstract

We study the collision dynamics of localized oscillons in two classes of $(1+1)$-dimensional scalar field theories with metastable false vacua, a normal class with a positive quartic self-interaction term and an inverted class with a negative quartic term. We construct small-amplitude oscillon solutions around the false vacuum using the Fodor {\emph{et al.}} expansion, and show that the force between oscillons decays exponentially at large separation, with a strength modulated by their relative phase. Numerical simulations of two-oscillon collisions exhibit reflection, crossing, and formation of excited oscillons. Resonance windows occur, similar to those found in kink-antikink collisions. In the normal theory, if the oscillons have sufficient energy, the field can pass over a sphaleron barrier and evolve into a kink-antikink pair, initiating a phase transition to the true vacuum. We also simulate the collision of oscillons evolved from a slightly perturbed sphaleron.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies collision dynamics of small-amplitude oscillons in two (1+1)-dimensional scalar theories with metastable false vacua (normal positive-quartic and inverted negative-quartic classes). Oscillons are constructed via the Fodor et al. perturbative expansion around the false vacuum; the inter-oscillon force is shown to decay exponentially with separation and to depend on relative phase. Numerical evolutions reveal reflection, crossing, excited-oscillon formation, and resonance windows analogous to kink-antikink scattering. In the normal theory the authors state that, for sufficient energy, collisions can surmount the sphaleron barrier and produce a kink-antikink pair that initiates a phase transition to the true vacuum; they also simulate collisions of oscillons evolved from a perturbed sphaleron.

Significance. If the energy-threshold claim holds, the work would identify a concrete channel for false-vacuum decay mediated by oscillon collisions, extending the well-studied kink-antikink resonance phenomenology to metastable potentials. The phase-dependent force and resonance-window results are of intrinsic interest for nonlinear field dynamics. The manuscript supplies no machine-checked proofs or parameter-free derivations, but the numerical exploration of multiple outcomes is a concrete contribution provided the simulations are adequately controlled.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'if the oscillons have sufficient energy, the field can pass over a sphaleron barrier and evolve into a kink-antikink pair' is load-bearing for the phase-transition result in the normal theory, yet the manuscript contains no explicit calculation showing that the energies of the Fodor et al. small-amplitude profiles exceed the sphaleron energy; because the expansion is perturbative in amplitude, the attainable energy is bounded by the regime of validity.
  2. [Numerical simulations] Numerical simulations section: no error bars, grid-convergence tests, or systematic parameter scans are reported for the collision evolutions; without these controls the robustness of the reported resonance windows and the kink-antikink formation channel cannot be assessed.
minor comments (2)
  1. [Introduction] The explicit forms of the two potentials (normal and inverted) should be stated in the introduction rather than deferred, to make the distinction between the two classes immediate.
  2. Figure captions for the collision snapshots should include the specific initial separation, relative phase, and total energy used in each run.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major points below and will revise the manuscript to incorporate the requested clarifications and controls.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'if the oscillons have sufficient energy, the field can pass over a sphaleron barrier and evolve into a kink-antikink pair' is load-bearing for the phase-transition result in the normal theory, yet the manuscript contains no explicit calculation showing that the energies of the Fodor et al. small-amplitude profiles exceed the sphaleron energy; because the expansion is perturbative in amplitude, the attainable energy is bounded by the regime of validity.

    Authors: We agree that an explicit energy comparison is needed to support the conditional claim. In the revised manuscript we will add a direct computation of the total energy for the small-amplitude Fodor profiles at the amplitudes used in our simulations, together with a comparison to the sphaleron barrier height. This will delineate the range of validity and indicate for which amplitudes the phase-transition channel becomes accessible. If the computed energies lie below the barrier we will qualify the statement accordingly while retaining the conditional phrasing. revision: yes

  2. Referee: [Numerical simulations] Numerical simulations section: no error bars, grid-convergence tests, or systematic parameter scans are reported for the collision evolutions; without these controls the robustness of the reported resonance windows and the kink-antikink formation channel cannot be assessed.

    Authors: We acknowledge the absence of reported numerical controls. In the revision we will include grid-convergence tests for representative two-oscillon collisions, provide error estimates on the locations of resonance windows, and add a limited parameter scan over initial separations and relative phases to demonstrate the robustness of the reflection, crossing, and phase-transition outcomes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from cited expansion and external numerics

full rationale

The paper constructs small-amplitude oscillon profiles via the externally cited Fodor et al. expansion and obtains all collision outcomes (reflection, resonance windows, kink-antikink formation) from direct numerical integration of the field equations. No load-bearing step equates a derived quantity to a fitted parameter or self-citation by construction; the sphaleron-barrier claim is an observed simulation result rather than an internal redefinition. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the standard existence of classical solutions to the nonlinear wave equation and the validity of the small-amplitude perturbative expansion; no new free parameters or invented entities are introduced beyond the model potentials already standard in the field.

axioms (2)
  • domain assumption Existence and stability of small-amplitude oscillon solutions around the false vacuum via the Fodor et al. expansion
    Invoked in the construction of initial conditions for collisions
  • domain assumption Classical evolution of the scalar field equation suffices to capture the reported dynamics
    Underlying all numerical simulations

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