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, K. F. Huang, and Y. F. Chen
Phys. Rev. E 95, 022214 – Published 21 February 2017

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.

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  • Received 10 August 2016
  • Revised 24 January 2017

DOI:https://doi.org/10.1103/PhysRevE.95.022214

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsGeneral Physics

Authors & Affiliations

Y. H. Hsieh, Y. T. Yu, P. H. Tuan, J. C. Tung, K. F. Huang, and Y. F. Chen

  • Department of Electrophysics, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 30010, Taiwan

  • *Corresponding author: yfchen@cc.nctu.edu.tw

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Vol. 95, Iss. 2 — February 2017

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