Visualization and comparison of classical structures and quantum states of four-dimensional maps
Visualization and comparison of classical structures and quantum states of four-dimensional maps
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DOI：
10.1103/physreve.89.022902
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发表时间：
2014-02-03
影响因子：
2.4
通讯作者：
Ketzmerick, Roland
中科院分区：
文献类型：
--
作者：
Richter, Martin;Lange, Steffen;Ketzmerick, Roland
对于一般的4D辛映射，我们建议使用3D相空间切片，这使得全球可视化的几何组织和共存的规则和混乱的运动。作为一个例子，我们考虑两个耦合的标准映射。的3D相空间切片的优点相比，标准的方法，如3D投影的轨道，频率分析，和混沌指标。量子力学，3D相空间切片允许的4D地图与经典相空间结构的本征态的胡西米函数的比较。这证实了4D映射的半经典本征函数假设。
For generic 4D symplectic maps we propose the use of 3D phase-space slices, which allow for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. As an example, we consider two coupled standard maps. The advantages of the 3D phase-space slices are presented in comparison to standard methods, such as 3D projections of orbits, the frequency analysis, and a chaos indicator. Quantum mechanically, the 3D phase-space slices allow for the comparison of Husimi functions of eigenstates of 4D maps with classical phase-space structures. This confirms the semiclassical eigenfunction hypothesis for 4D maps.