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arXiv · 2008.04610

Symmetry breaking in a two-component system with repulsive interactions and linear coupling

Hidetsugu Sakaguchi·Boris A. Malomed
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Abstract

We extend the well-known theoretical treatment of the spontaneous symmetry breaking (SSB) in two-component systems, combining linear coupling and self-attractive nonlinearity, to a system in which the linear coupling competes with repulsive interactions. First, we address one- and two-dimensional (1D and 2D) ground-state (GS) solutions and 2D vortex states with topological charges S=1 and 2, maintained by a confining harmonic-oscillator potential. The system can be implemented in BEC and optics. By means of the Thomas-Fermi approximation and numerical solution of the underlying coupled Gross-Pitaevskii equations, we demonstrate that SSB takes place, in the GSs and vortices alike, when the cross-component repulsion is stronger that the self-repulsion in each component. The SSB transition is categorized as a supercritical bifurcation, which gives rise to states featuring broken symmetry in an inner area, and intact symmetry in a surrounding layer. Unlike stable GSs and vortices with S=1, the states with S=2 are unstable against splitting. We also address SSB for 1D gap solitons in the system including a lattice potential. In this case, SSB takes place under the opposite condition, i.e., the cross-component repulsion must be weaker than the self-repulsion, and SSB is exhibited by antisymmetric solitons.

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Hidetsugu Sakaguchi, Boris A. Malomed. 2020-08-11. Symmetry breaking in a two-component system with repulsive interactions and linear coupling. https://arxiv.org/abs/2008.04610

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