Novaes M, Pedrosa J M, Wisniacki D, Carlo G G, Keating J P
School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):035202. doi: 10.1103/PhysRevE.80.035202. Epub 2009 Sep 15.
We present an approach to calculating the quantum resonances and resonance wave functions of chaotic scattering systems, based on the construction of states localized on classical periodic orbits and adapted to the dynamics. Typically only a few such states are necessary for constructing a resonance. Using only short orbits (with periods up to the Ehrenfest time), we obtain approximations to the longest-living states, avoiding computation of the background of short living states. This makes our approach considerably more efficient than previous ones. The number of long-lived states produced within our formulation is in agreement with the fractal Weyl law conjectured recently in this setting. We confirm the accuracy of the approximations using the open quantum baker map as an example.
我们提出了一种计算混沌散射系统的量子共振和共振波函数的方法，该方法基于构建定域在经典周期轨道上并适应动力学的态。通常，构建一个共振仅需要少数几个这样的态。仅使用短轨道（周期至多为埃伦费斯特时间），我们就能得到寿命最长的态的近似值，避免了对短寿命态背景的计算。这使得我们的方法比之前的方法效率大幅提高。我们公式中产生的长寿命态的数量与最近在此背景下推测的分形韦尔定律相符。我们以开放量子面包师映射为例，证实了这些近似值的准确性。
