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Avoided level crossings in an elliptic billiard

Title
Avoided level crossings in an elliptic billiard
Authors
Kim, Ji HwanKim, Jae WonYi, Chang HwanYu, Hyeon HyeLee, Ji WonKim, Chil-Min
DGIST Authors
Kim, Ji Hwan; Kim, Jae Won; Yi, Chang Hwan; Yu, Hyeon Hye; Lee, Ji Won; Kim, Chil-Min
Issue Date
2017-10
Citation
Physical Review E, 96(4)
Type
Article
Article Type
Article
Keywords
EigenvaluesModesMotionPeriodic-OrbitsQuantumScarsSpectrumStationarySystemsTransition
ISSN
2470-0045
Abstract
In an elliptic billiard, we find avoided level crossings taking place over wide ranges, which are of a Demkov type for generations of eigenfunctions localized on an islands chain and its pair unstable periodic orbit. For a proof of the existence of avoided level crossings, first, we show that the quantized eigenvalue of the unstable periodic orbit, obtained by the Einstein-Brillouin-Keller quantization rule, passes the eigenvalues of bouncing-ball modes localized on the unstable periodic orbit after Demkov type avoided level crossings so that pairs of bouncing-ball modes are sequentially generated. Next, by using a perturbed Hamiltonian, we show that off-diagonal elements in Hamiltonian are nonzero, which give rise to an interaction between two eigenfunctions. Last, we verify that the observed phenomenon is Fermi resonance: that is, the quantum number difference of two normal modes equals the periodic orbits, where eigenfunctions are localized after an avoided level crossing.
URI
http://hdl.handle.net/20.500.11750/4721
DOI
10.1103/PhysRevE.96.042205
Publisher
AMER PHYSICAL SOC
Files:
There are no files associated with this item.
Collection:
Emerging Materials ScienceETC1. Journal Articles
DGIST-ETH Microrobot Research Center1. Journal Articles
Emerging Materials ScienceETC1. Journal Articles
ETC1. Journal Articles


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