Spontaneous symmetry and antisymmetry breaking in a ring with two potential barriers

TL;DR

This paper investigates spontaneous symmetry and antisymmetry breaking in a nonlinear Schrödinger system with potential barriers on a ring, revealing bifurcation phenomena and stable asymmetric solutions relevant to optics and BEC.

Contribution

It introduces a fundamental model for SSB and SASB in a ring with barriers, providing analytical, numerical, and exact solutions, and explores bifurcation mechanisms in nonlinear systems.

Findings

SSB occurs via supercritical bifurcation in attractive systems.

SASB destabilizes antisymmetric states in repulsive systems.

Stable asymmetric solutions are explicitly constructed.

Abstract

We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic term, respectively, on a one-dimensional ring split in two mutually symmetric boxes by delta-functional potential barriers, placed at opposite points. The system is relevant to optics and BEC. The spectrum of the linearized system is found in analytical and numerical forms. SSB and SASB are predicted by dint of the variational approximation, and studied in the numerical form. A particular stable solution, which demonstrates strong asymmetry, is found in an exact form. In the system with the attractive nonlinearity, the SSB of the symmetric ground state is initiated by the modulational instability. It creates stationary asymmetric states through a supercritical bifurcation. In the self-repulsive system, SASB makes the lowest antisymmetric excited state unstable, transforming it into an antisymmetry-breaking oscillatory mode.