Maslov indices in the Gutzwiller trace formula
Maslov indices in the Gutzwiller trace formula
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Gutzwiller 迹公式中的马斯洛夫指数
DOI：
10.1088/0951-7715/4/2/007
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发表时间：
1991
期刊：
影响因子：
1.7
通讯作者：
J. Robbins
中科院分区：
文献类型：
--
作者：
J. Robbins
Gutzwiller迹公式是束缚量子系统的态密度的半经典近似，用对应经典系统的周期轨道之和表示。作者建立了与经典周期轨道相关的拓扑不变量的存在性，即它们的不变流形的缠绕数，并证明了这个缠绕数正是迹公式中出现的指数。这个证明在任何维数下都是有效的。给出了该指数的显式计算公式。
The Gutzwiller trace formula is a semi-classical approximation for the density of states of a bound quantum system, expressed in terms of a sum over periodic orbits of the corresponding classical system. The authors establish the existence of a topological invariant associated with classical periodic orbits, namely the winding number of their invariant manifolds, and show that this winding number is precisely the index which appears in the trace formula. The proof is valid in any number of dimensions. Explicit formulae for the index are given.