Extracting trajectory equations of classical periodic orbits from the quantum eigenmodes in two-dimensional integrable billiards

Y. H. Hsieh, Y. T. Yu, P. H. Tuan, J. C. Tung, Kai-Feng Huang, Yung-Fu Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The trajectory equations for classical periodic orbits in the equilateral-triangular and circular billiards are systematically extracted from quantum stationary coherent states. The relationship between the phase factors of quantum stationary coherent states and the initial positions of classical periodic orbits is analytically derived. In addition, the stationary coherent states with noncoprime parametric numbers are shown to correspond to the multiple periodic orbits, which cannot be explicable in the one-particle picture. The stationary coherent states are further verified to be linked to the resonant modes that are generally observed in the experimental wave system excited by a localized and unidirectional source. The excellent agreement between the resonant modes and the stationary coherent states not only manifests the importance of classical features in experimental systems but also paves the way to manipulate the mesoscopic wave functions localized on the periodic orbits for applications.

Original languageEnglish
Article number022214
JournalPhysical Review E
Volume95
Issue number2
DOIs
StatePublished - 21 Feb 2017

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