arXiv subjects

N. S. Manton

Publications and source records attributed to N. S. Manton.

At least 19 recordsLinked to original sources

arXiv2026

Circle of Alpha-Particle Cluster Shapes in Neon-20

Quantum states of Neon-20 are generally agreed to lie in rotational-vibrational bands of a cluster of five alpha particles. However, more than one cluster shape has been proposed as dominant at low energy. As relative motion within a cluster is soft in certain directions, we investigate how the low-lying rotational bands of Neon-20 can arise from a circle of clusters connecting favoured shapes: a triangular bipyramid, a square pyramid, and a $D_{2d}$-symmetric distorted tetrahedron -- a twisted bow-tie. Motion around the circle extends the Berry pseudo-rotation that connects differently oriented bipyramids.

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arXiv2026

Collision Dynamics of False-Vacuum Oscillons

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.

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arXiv2025

Coulomb-Corrected Wormhole Model for Neon-20

Building on the spatial wormhole geometry proposed by Manton and Dunajski, we develop a modified model for the Neon-20 nucleus that incorporates a repulsive Coulomb potential. This reduces the large threshold energy for cluster break-up in the original model and converts most bound states to resonances. We use generalized WKB methods to calculate the energies of bound states, and also the energies and widths of under-barrier and over-barrier resonances. The results align closely with experimental data for the 0_1^+ , 0_1^- and 0_4^+ rotational bands of Neon-20, including the large widths in the higher-nodal 0_4^+ band.

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arXiv2025

A ${\mathbb{CP}}^2$ SMEFT

An extension of the Standard Model is proposed, where the Higgs field is valued in the complex projective plane ${\mathbb{CP}}^2$, rather than ${\mathbb{C}}^2$. Its geometry is consistent with $U(2) \simeq (SU(2) \times U(1))/ \mathbb{Z}_2$ electroweak gauge symmetry. The leading terms in the Lagrangian, beyond those of the Standard Model, are much more tightly constrained than in general SMEFTs, and the custodial $SO(4)$ symmetry of the Higgs sector is mildly broken. The predicted tree-level deviations from Standard Model phenomenology depend on a single large mass parameter $M$. Current experimental data imply that $M$ is a few TeV or larger.

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arXiv2025

Approach to nuclear cross sections via classical Skyrmion scattering: A proposal

By analogy with heavy ion collisions, which can be modelled by a classical hydrodynamics, it is proposed that the differential cross section for collisions of smaller nuclei can be calculated from the classical, numerical scattering data for Skyrmions. It is also suggested that the numerical data for the outgoing particles should be classified into bins, as is done in nuclear physics experiments.

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arXiv2025

Dynamics of Excited BPS 3-Vortices

We analyze the dynamics of BPS 3-vortex solutions. First, for unexcited vortices, we study the 2-dimensional moduli space of centred vortices with $y \to -y$ symmetry, and its metric. We identify the 1-dimensional subspaces describing the head-on collisions of equidistant collinear and equilateral triangle configurations, where geodesic motion results in $90^\circ$ and 60^\circ$ scattering, respectively. Second, by studying the frequency spectrum of vibrational shape modes along these subspaces, we explain how the force-free, geodesic motion is modified by shape mode excitations into a pattern of chaotic multi-bounce collisions.

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arXiv2024

Antikink-Kink Forces Revisited

We recalculate the force exerted by an antikink on a kink when their overlapping tail fields are close to either a quadratic or quartic minimum of the field theory potential. Our uniform method of calculation exploits the modified Bogomolny equation satisfied by an accelerating kink. This method has been used before in special cases, but is shown here to have broad applicability.

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arXiv2024

Collective Coordinate Models for 2-Vortex Shape Mode Dynamics

Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space $M$, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on $M$, modified by a potential, when the mode oscillations are fast relative to the moduli space motion and their amplitudes are small. When the lowest-frequency mode is excited with a large amplitude, the geodesic flow is not a correct description. Instead, a chaotic, or even fractal, multi-bounce structure in vortex-vortex collisions is predicted.

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arXiv2024

Robustness of the Hedgehog Skyrmion

We investigate the radial profile function of the hedgehog Skyrmion with unit baryon number in generic EFTs (effective field theories) of pions. The analysis assumes chiral symmetry and ignores the pion mass term. The Skyrmion is always smooth, because it has no point source at the origin, and terms in the EFT with higher numbers of pion derivatives do not result in uncontrolled large corrections or singularities there. The profile varies in quite a limited way as the terms in the EFT change, and a universal profile function is proposed.

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arXiv2023

Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space

The flow of shape eigenmodes of the small fluctuation operator around BPS 2-vortex solutions is calculated, as a function of the intervortex separation $2d$. For the rotationally-invariant 2-vortex, with $d = 0$, there are three discrete modes; the lowest is non-degenerate and the upper two are degenerate. As $d$ increases, the degeneracy splits, with one eigenvalue increasing and entering the continuous spectrum, and the other decreasing and asymptotically coalescing with the lowest eigenvalue, where they jointly become the eigenvalue of the 1-vortex radial shape mode. The behaviour of the eigenvalues near $d=0$ is clarified using a perturbative analysis, and also in light of the 2-vortex moduli space geometry.

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arXiv2023

Integration Theory for Kinks and Sphalerons in One Dimension

The static kink, sphaleron and kink chain solutions for a single scalar field $ϕ$ in one spatial dimension are reconsidered. By integration of the Euler--Lagrange equation, or through the Bogomolny argument, one finds that each of these solutions obeys a first-order field equation, an autonomous ODE that can always be formally integrated. We distinguish the BPS case, where the required integral is along a contour in the $ϕ$-plane, from the semi-BPS case, where the integral is along a contour in the Riemann surface double-covering the $ϕ$-plane, and is generally more complicated.

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arXiv2023

Neumann Boundary Condition for Abelian Vortices

We study abelian BPS vortices on a surface $S$ with boundary, which satisfy the Neumann boundary condition on the norm of the scalar field, or equivalently, that the current along the boundary vanishes. These vortices have quantised magnetic flux and quantised energy. Existence of such vortices is manifest when $S$ is the quotient by a reflection of a smooth surface without boundary, for example a hemisphere. The $N$-vortex moduli space then admits an interesting stratification, depending on the number of vortices in the interior of $S$ and the number of half-vortices on the boundary.

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arXiv2023

The Simplest Oscillon and its Sphaleron

Oscillons in a simple, 1-dimensional scalar field theory with a cubic potential are discussed. The theory has a classical sphaleron, whose decay generates a version of the oscillon. A good approximation to the small-amplitude oscillon is constructed explicitly using the asymptotic expansion of Fodor et al., but for larger amplitudes a better approximation uses the discrete, unstable and stable deformation modes of the sphaleron.

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arXiv2022

Quantum Statistical Mechanics of Dissolving Vortices

The quantum partition function for dissolving Abelian Higgs vortices is calculated explicitly, using spectral data for the Beltrami Laplacian on the $N$-vortex moduli space $\mathbb{CP}^N$ with a scaled Fubini--Study metric. From the partition function, the pressure of the vortex gas is derived. There are three asymptotic regimes -- High, Intermediate and Low Temperature. The phase crossover from Intermediate to Low Temperature is modelled by a Bessel function. In the Low Temperature regime the free energy is not extensive but is proportional to $N^2$.

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arXiv2022

Quantum Statistical Mechanics of Vortices

The asymptotic partition function for quantized Abelian Higgs vortices at high temperature $T$ is found to leading and subleading order, and from this the equation of state of the vortex gas is derived, including the first quantum correction. It is assumed that the Hamiltonian is proportional to the Laplace--Beltrami operator on the moduli space of static $N$-vortex solutions. The partition function is calculated using the total volume and total scalar curvature of the moduli space.

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arXiv2022

Relativistic Moduli Space for Kink Collisions

The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections {\it perturbatively} in kink scattering. It gives an excellent description of kink-antikink collisions in $ϕ^4$ field theory already at first order, and at higher order, reproduces the fractal structure in the formation of the final state with an error of only $4\%$.

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arXiv2021

Collective coordinate model of kink-antikink collisions in $ϕ^4$ theory

The fractal velocity pattern in symmetric kink-antikink collisions in $ϕ^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode usefully approximates Lorentz contractions of the kink and antikink, and the previously problematic null-vector in the shape mode amplitude at zero separation is regularized.

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arXiv2020

Kink Moduli Spaces -- Collective Coordinates Reconsidered

Moduli spaces - finite-dimensional, collective coordinate manifolds - for kinks and antikinks in $ϕ^4$ theory and sine-Gordon theory are reconsidered. The field theory Lagrangian restricted to moduli space defines a reduced Lagrangian, combining a potential with a kinetic term that can be interpreted as a Riemannian metric on moduli space. Moduli spaces should be metrically complete, or have an infinite potential on their boundary. Examples are constructed for both kink-antikink and kink-antikink-kink configurations. The naive position coordinates of the kinks and antikinks sometimes need to be extended from real to imaginary values, although the field remains real. The previously discussed null-vector problem for the shape modes of $ϕ^4$ kinks is resolved by a better coordinate choice. In sine-Gordon theory, moduli spaces can be constructed using exact solutions at the critical energy separating scattering and breather (or wobble) solutions; here, energy conservation relates the metric and potential. The reduced dynamics on these moduli spaces accurately reproduces properties of the exact solutions over a range of energies.

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