标题： 在旋转双阱势中的非线性模式和对称性破缺 显示英文标题

标题： Nonlinear modes and symmetry breaking in rotating double-well potentials

摘要： 我们研究了被困在旋转环中的模式，该环携带自聚焦（SF）或非聚焦（SDF）三次非线性以及双井势$\cos^{2}\theta $，其中$\theta $是角坐标。 基于旋转参考系中非线性薛定谔（NLS）方程的模型描述了扭曲管道波导中的光传播以及其他光学设置，并且还描述了被困在环形结构中并受旋转势拖动的玻色-爱因斯坦凝聚体（BEC）。 在SF和SDF状态下，分别发现了五种和四种具有不同对称性的被困模式。 在第一旋转布里渊区中研究了这些模式的形状和稳定性及其之间的转变。 在SF状态下，发现了两种对称性破坏转变，分别是次临界和超临界类型。 在SDF状态下，发生了一种反对称性破坏转变。 在SF和SDF系统中均识别出基态。 显示英文摘要

摘要： We study modes trapped in a rotating ring carrying the self-focusing (SF) or defocusing (SDF) cubic nonlinearity and double-well potential $\cos^{2}\theta $, where $\theta $ is the angular coordinate. The model, based on the nonlinear Schr\"{o}dinger (NLS) equation in the rotating reference frame, describes the light propagation in a twisted pipe waveguide, as well as in other optical settings, and also a Bose-Einstein condensate (BEC)trapped in a torus and dragged by the rotating potential. In the SF and SDF regimes, five and four trapped modes of different symmetries are found, respectively. The shapes and stability of the modes, and transitions between them are studied in the first rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions are found, of subcritical and supercritical types. In the SDF regime, an antisymmetry-breaking transition occurs. Ground-states are identified in both the SF and SDF systems.