论文标题
关于具有磁场的3D轴对称非群体类型系统的可扩散性
On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields
论文作者
论文摘要
我们扩展了对非零磁场和轴向对称性的三维（3D）哈密顿型系统的研究，即圆形抛物线病例，即圆形的球体病例和呈尖粒球体。更确切地说，我们专注于线性和一些二次分类性的特殊情况。在线性案例中，没有任何新的可整合系统出现。在二次情况下，我们发现了一个新的最低促进系统，该系统位于圆形抛物线和圆柱形病例的相交，而另一个则位于圆柱形，球形，扁平球形和pr酸球体的相交中。通过对这些系统施加其他条件，我们发现了每个四二次最小化的系统，一个新的无限高阶最大促进系统的家族。这两个系统通过时间依赖性的规范变换分别与笼子和谐波振荡器没有磁场的链接和谐波振荡。
We extend the investigation of three-dimensional (3D) Hamiltonian systems of non-subgroup type admitting non-zero magnetic fields and an axial symmetry, namely the circular parabolic case, the oblate spheroidal case and the prolate spheroidal case. More precisely, we focus on linear and some special cases of quadratic superintegrability. In the linear case, no new superintegrable system arises. In the quadratic case, we found one new minimally superintegrable system that lies at the intersection of the circular parabolic and cylindrical cases and another one at the intersection of the cylindrical, spherical, oblate spheroidal and prolate spheroidal cases. By imposing additional conditions on these systems, we found for each quadratically minimally superintegrable system a new infinite family of higher-order maximally superintegrable systems. These two systems are linked respectively with the caged and harmonic oscillators without magnetic fields through a time-dependent canonical transformation.
