标题： 弯曲一维玻色-爱因斯坦凝聚体中暗孤子的动力学 显示英文标题

标题： Dynamics of a dark soliton in a curved 1D Bose-Einstein condensate

摘要： 我们研究了在一维玻色-爱因斯坦凝聚体中，受限于弯曲几何结构的暗孤子的非线性动力学。利用曲线坐标系中的Gross-Pitaevskii方程和局部曲率的微扰展开，我们推导出了孤子速度和曲率的耦合演化方程。对于常数曲率的情况，如圆形几何结构，孤子动力学仅由初始速度和曲率决定。值得注意的是，孤子在曲率两个数量级范围内沿几乎恒定的角轨迹运动，这表明存在一个与初始速度无关的涌现守恒量。我们将分析扩展到具有空间变化曲率的椭圆轨迹，并表明孤子动力学仍由局部曲率分布决定。在这种情况下，有效常数曲率模型在局部曲率具有平滑变化时能准确描述动力学。当孤子穿过快速曲率变化和/或非单调行为区域时，该模型无法准确描述孤子动力学，尽管整体行为仍可完全映射到曲率分布。我们的结果为理解几何在孤子动力学中的作用提供了定量框架，并为未来在弯曲量子系统中研究非线性激发铺平了道路。 显示英文摘要

摘要： We investigate the nonlinear dynamics of dark solitons in a one-dimensional Bose-Einstein condensate confined to a curved geometry. Using the Gross-Pitaevskii equation in curvilinear coordinates and a perturbative expansion in the local curvature, we derive a set of coupled evolution equations for the soliton velocity and the curvature. For the case of constant curvature, such as circular geometries, the soliton dynamics is governed solely by the initial velocity and curvature. Remarkably, the soliton travels a nearly constant angular trajectory across two orders of magnitude in curvature, suggesting an emergent conserved quantity, independent of its initial velocity. We extend our analysis to elliptical trajectories with spatially varying curvature and show that soliton dynamics remain determined by the local curvature profile. In these cases, the model of effective constant curvature describes accurately the dynamics given the local curvature has smooth variation. When the soliton crosses regions of rapid curvature variation and/or non-monotonic behavior, the model fails to describe to soliton dynamics, although the overall behavior can still be fully mapped to the curvature profile. Our results provide a quantitative framework for understanding the role of geometry in soliton dynamics and pave the way for future studies of nonlinear excitations in curved quantum systems.