Wave functions with localizations on classical periodic orbits in weakly perturbed quantum billiards

C. C. Liu*, T. H. Lu, Yung-Fu Chen, Kai-Feng Huang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We analytically investigate quantum wave functions with localizations on classical periodic orbits (POs) in the circular billiards. We construct the coherent states which are the coherent superpositions of nearly degenerate eigenstates and found to be localized around single classical POs. With the constructed coherent states, we can analytically express the mesoscopic eigenstates in the weakly perturbed systems, which are found to be localized on the ensemble of classical POs. Furthermore, these coherent states can be utilized to study the quantum vortex structures in quantum billiards.

Original languageEnglish
Article number046214
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number4
DOIs
StatePublished - 1 Jan 2006

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