Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

Original languageEnglish
Article number012217
Number of pages8
JournalPhysical Review E
Volume95
Issue number1
DOIs
StatePublished - 30 Jan 2017

Keywords

  • SIMPLE METAL-CLUSTERS
  • WAVE-FUNCTIONS
  • PHYSICS
  • EIGENFUNCTIONS
  • SCARS
  • STATE

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