Hamiltonian bifurcation theory of closed orbits in the diamagnetic Kepler problem.
Hamiltonian bifurcation theory of closed orbits in the diamagnetic Kepler problem.
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DOI：
10.1103/physreva.45.1746
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发表时间：
1992-02
期刊：
影响因子：
--
通讯作者：
J.-M. Mao;J. Delos
中科院分区：
文献类型：
--
作者：
J.-M. Mao;J. Delos
经典混沌系统具有周期轨道的扩散。这种现象是通过测量氢原子在磁场中的吸收光谱在量子系统中观察到的。本文对原子中电子在磁场中的周期轨道或闭合轨道的分岔给出了理论解释。我们的问题是，随着能量的变化，如何从现有的周期轨道中创造出新的周期轨道，或者“不知从哪里冒出来”。哈密顿分岔理论给出了答案：它断言在具有两个自由度的保守系统中只存在五种典型的分岔类型。我们将展示每种类型的一个示例。我们所研究的每一个案例都属于该理论所描述的模式之一。
Classically chaotic systems possess a proliferation of periodic orbits. This phenomenon was observed in a quantum system through measurements of the absorption spectrum of a hydrogen atom in a magnetic field. This paper gives a theoretical interpretation of the bifurcations of periodic or closed orbits of electrons in atoms in magnetic fields. We ask how new periodic orbits can be created out of existing ones or ``out of nowhere'' as the energy changes. Hamiltonian bifurcation theory provides the answer: it asserts the existence of just five typical types of bifurcation in conservative systems with two degrees of freedom. We show an example of each type. Every case we have examined falls into one of the patterns described by the theory.