Spontaneous symmetry breaking in dual-core baby-Skyrmion systems

Abstract

We introduce a system composed of two (2+1)-dimensional baby-skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core models previously studied\ in nonlinear optics and BEC, here the symmetry-breaking bifurcation (SBB) in solitons (baby skyrmions) occurs with the increase of the inter-core coupling ($\kappa$), rather than with its decrease, due to the fact that even in the uncoupled system neither core may be empty. Prior to the onset of the symmetry breaking between the two components of the solitons, they gradually separate in the lateral direction, due to the increase of $\kappa$, which is explained in an analytical form by means of an effective interaction potential. Such evolution scenario are produced for the originally symmetric states with topological charges in the two cores $\left(B^{(1)},B^{(2)}\right)$, with $% B^{(1)}=B^{(2)}=1,2,3,4$. The evolution of mixed states, of the $\left(1,2\right)$ and $\left(2,4\right)$ types, with the variation of $\kappa$ is studied too.Comment: 17 pages, 18 figures, clarifications and a reference added; final version appearing in PR

Magnetothermodynamics of BPS baby skyrmions

“…To overcome the computational difficulties and learn something about the electromagnetic properties of BPS Skyrme type solitons, one can analyze lower-dimensional analogs, as has been done successfully already in many occasions. In fact, there exists a (2 + 1) dimensional version of the Skyrme model, usually referred to as the baby Skyrme model, which supports solitonic solutions (baby skyrmions) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] (for the gauged version see [39,40]). This field theory also possesses its BPS limit, whose Lagrangian consists of the (2+1) dimensional version of the Skyrme term and a potential [41][42][43].…”

Bessel Vortices in Spin-Orbit-Coupled Binary Bose-Einstein Condensates with Zeeman Splitting

“…In this study, both the ground and excited states can be obtained by NN. In particular, the NN solutions produce 2D ("baby" [38,39,40]) skyrmions in the SO-coupled BEC (note that a baby skyrmion in a three-component condensate was created experimentally [41]). The corresponding values of the skyrmion number can be calculated analytically.…”

Topological phase transitions in the gauged BPS baby Skyrme model

“…The baby Skyrme model [1] (see also [2]- [12]) is a lower dimensional version of the 3 + 1 dimensional Skyrme model [14], that is, an effective theory of the low energy, nonperturbative sector of Quantum Chromodynamics. It plays an important role as a toy model for the higher dimensional theory.…”