AI 中文总结
受莱斯特 - 维格曼猜想启发，研究环面上圆流动力学，证明类似消失相关性猜想成立，有面积可观测量的混合，还确定了全局及局部区域中面积的概率密度函数。
AI 中文摘要
受关于半径不断增大的圆边界附近格点的莱斯特 - 维格曼消失面积相关性猜想的启发，我们研究环面上圆流的动力学（这与环面上磁场中带电粒子的运动有关）。我们表明在这种情况下消失相关性猜想的类似情况成立，即尽管流本质上是可积的，但我们有“面积可观测量的混合”。我们还确定了全局和局部区域中面积的概率密度函数。
英文摘要
Motivated by the Lester-Wigman vanishing area correlation conjecture for lattice points near the boundary of circles of growing radius, we investigate the dynamics of circle flows on tori (which are related to the motion of a charged particle in a magnetic field on a torus.) We show that an analogue of the vanishing correlation conjecture holds in this setting, i.e., we have "mixing for the area observable" despite the flow being essentially integrable. We also determine the probability density function of the areas, in global as well as local regimes.
Comments30 pages, 1 figure
