Time-dependent Bogomolny-Prasad-Sommerfeld skyrmions

Ioannidou, Theodora; Lukács, Árpád

doi:10.1063/1.4940695

Cited by 10 publications

(15 citation statements)

References 23 publications

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“…This ansatz is compatible with the full four-dimensional Euler-Lagrange equations and leads to the reduced action [40] …”

Section: A Small Perturbation Approximation -Oscillating Modesmentioning

confidence: 75%

“…2. Potential U = (1 − cos ξ) 6 As mentioned already, resonance modes for the class of potentials U = (1 − cos ξ) α , α > 3, have been studied numerically in [40]. So, for completeness, let us also analyze the potential U = (1 − cos ξ) 6 .…”

Section: Resonances For the Potentialsmentioning

confidence: 99%

“…From the full non-linear simulation we get the results shown in Table 2. This should be compared to the values reported in [40], Ω IL 1 = 4.71 and T IL 1 = 0.83. We find that the half-lives (decay widths) essentially agree, whereas there is a difference of about 10% for the frequencies.…”

Section: Resonances For the Potentialsmentioning

confidence: 99%

“…Physically, they correspond to exponentially damped vibrations in a classical context or to unstable bound states (resonances) in a quantum description. [We remark that resonance modes within the BPS Skyrme model for a certain class of potentials have been studied numerically in [40].] Finally, the full nonlinear time evolution may be investigated for the classical field theory.…”

Section: Arxiv:160704286v2 [Hep-th] 19 Sep 2016mentioning

confidence: 99%

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Radial vibrations of BPS skyrmions

et al. 2016

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We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate description of this resonance. Further, for many potentials additional higher resonances appear, again in agreement with known experimental results.

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“…This ansatz is compatible with the full four-dimensional Euler-Lagrange equations and leads to the reduced action [40] …”

Section: A Small Perturbation Approximation -Oscillating Modesmentioning

confidence: 75%

Section: Resonances For the Potentialsmentioning

confidence: 99%

Section: Resonances For the Potentialsmentioning

confidence: 99%

Section: Arxiv:160704286v2 [Hep-th] 19 Sep 2016mentioning

confidence: 99%

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Radial vibrations of BPS skyrmions

et al. 2016

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“…For that reason, generalized Skyrme models [2] that saturate the Bogomolny bound have been studied extensively since their mass is roughly proportional to the baryon number. Recently in [3], a submodel of the generalized Skyrme model has been considered, which consists, only, of the square of the baryon current and a potential term. This model is called the BPS Skyrme model since a Bogomolny bound exists and a static solution saturates it.…”

Section: Introductionmentioning

confidence: 99%

Discrete BPS skyrmions

Agaoglou

Charalampidis

Ioannidou

et al. 2017

Journal of Mathematical Physics

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A discrete analogue of the extended Bogomolny-Prasad-Sommerfeld (BPS) Skyrme model that admits time-dependent solutions is presented. Using the spacing h of adjacent lattice nodes as a parameter, we identify the spatial profile of the solution and the continuation of the relevant branch of solutions over the lattice spacing for different values of the potential (free) parameter α. In particular, we explore the dynamics and stability of the obtained solutions, finding that, while they generally seem to be prone to instabilities, for suitable values of the lattice spacing and for sufficiently large value of α, they may be long-lived in direct numerical simulations. *

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Roper resonances and quasi-normal modes of Skyrmions

Adam

Haberichter

Romańczukiewicz

et al. 2018

J. High Energ. Phys.

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Radial vibrations of charge one hedgehog Skyrmions in the full Skyrme model are analysed. We investigate how the properties of the lowest resonance modes (quasi normal modes) -their frequencies and widths -depend on the form of the potential (value of the pion mass as well as the addition of further potentials) and on the inclusion of the sextic term. Then we consider the inverse problem, where certain values for the frequencies and widths are imposed, and the field theoretic Skyrme model potential giving rise to them is reconstructed. This latter method allows to reproduce the physical Roper resonances, as well as further physical properties of nucleons, with high precision.PACS numbers: I. INTRODUCTIONThe Skyrme model [1] is an effective field theory (EFT) which bridges the underlying fundamental theory, Quantum Chromodynamics (QCD) -well understood in the perturbative, high energy regime -with the non-perturbative low energy region, beyond a scale where confinement and hadronisation leave only color-less states as observable particles. The natural field degrees of freedom in this regime are the lightest quasi-particles i.e., pions. The main attractiveness of the model originates from the fact that this field content is sufficient to describe, in principle, all other excitations -baryons and atomic nuclei -which emerge as non-perturbative states in such a mesonic fluid, or in the modern language, as topological solitons.This solitonic framework received further support from the large N c limit where it has been rigorously shown that QCD can be described by a weakly interacting theory of mesons [2]. Moreover, the pertinent topological index of the Skyrme model has been identified with the baryon charge. Finally, after the semiclassical quantization of zero modes of the classical solutions of the Skyrme model (Skyrmions) in a given topological sector (baryon charge) one got access to fermionic excitations of this classically purely bosonic theory. This opened the way for a realistic application of the Skyrme model for the description of baryons [3], [4] (proton, neutron, ∆ resonances), lighter nuclei and their excitation bands [5], [6] as well as higher nuclei, binding energies [7]-[9] and even infinite nuclear matter which defines properties of neutron stars [10], [11].In the baryon number one sector and with the SU(2) flavor group, there are two simple types of degrees of freedom of nucleons whose excitations can lead to new quasiparticles. First of all, an (iso)rotational excitation explains the ∆ resonance. Another possibility is to excite some vibrational degrees of freedom. This leads to new states which carry the same spin and isospin quantum numbers as the nucleons, i.e., the Roper resonances. The first three reasonably well established Ropers on top of the nucleons are: N (1440), N (1710), N (1880), which are highly short-living quasiparticles. Specifically, the first Roper N (1440) has a relatively wide Breit-Wigner width Γ = 300 MeV (and quite short mean life time τ = /Γ). While for the next two we hav...

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Time-dependent Bogomolny-Prasad-Sommerfeld skyrmions

Cited by 10 publications

References 23 publications

Radial vibrations of BPS skyrmions

Radial vibrations of BPS skyrmions

Discrete BPS skyrmions

Roper resonances and quasi-normal modes of Skyrmions

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