Isospinning hopfions

Abstract

The problem of constructing internally rotating solitons of fixed angular frequency ω in the Faddeev-Skyrme model is reformulated as a variational problem for an energylike functional, called pseudoenergy, which depends parametrically on ω. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on ω, and on their conserved total isospin J, studied. It is found that, generically, the shape of a soliton is independent of ω, and that its size grows monotonically with ω. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.

Oscillons in a perturbed signum-Gordon model

“…For example, small amplitude radial perturbations of static solitons contribute to some vibrational states, which have been interpreted as the Roper resonances [23][24][25][26][27][28][29][30][31][32][33][34][35]. Furthermore, (iso)-rotations influence shapes of Skyrmions and so can change their moments of inertia which in turn can modify the energies of quantum states [36][37][38][39][40]. Finally, scattering of Skyrmions [41,42] can be interpreted as scattering of atomic nuclei (heavy ions) and teach us some physics of fusion/fission processes.…”

Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model

“…Further increase of the gauge coupling leads to shrinkage of the Hopfion, and the magnetic field effectively squeezes the configuration. This effect is opposite to the isorotations of the Hopfions, which also affect the structure of the solutions [39,40].…”

Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential

“…In the model with the simple potential term, which breaks global SO(3) symmetry [29][30][31][32], the structure of the solutions of the massive Faddeev-Skyrme model is not very much different from the JHEP09(2017)029 massless case. Note also the modification of the model via inclusion other 4th order on derivative terms does not change this pattern [42].…”

“…In the paper by Foster [29] the Faddeev-Skyrme model with an SO(3) symmetry breaking potential, which is similar to the usual pion mass potential of the Skyrme model, was considered in the limit of the infinite mass. The effect of this term for the axially symmetric configurations of lowest degrees was investigated in earlier work [30] Note that potential of that type, was also used to stabilize the classically isospinning Hopfions [31,32]. The double vacuum potential in the Faddeev-Skyrme model with a potential term with two discrete vacua was considered in [33].…”

“…This is the solution with dihedral symmetry, see the corresponding plots in table 1. Recall that in the massless Faddeev-Skyrme model the link L 1,1 2,2 is the minimal energy charge six solution [40] whereas in the presence of the usual mass term the global minimum is the axially symmetric Hopfion A 3,2 [31,32].…”