PT symmetric Aubry–Andre model

PT symmetric Aubry–Andre model describes an array of N coupled optical waveguides with position-dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of quasi-periodicity for small number of lattice sites. We obtain the Hofstadter butterfly spectrum and...

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Bibliographic Details
Published in:Physics letters. A 2014-06, Vol.378 (30-31), p.2024-2028
Main Author: Yuce, C.
Format: Article
Language:English
Subjects:
Non-Hermitian Hamiltonian
PT symmetric optical system
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Summary:PT symmetric Aubry–Andre model describes an array of N coupled optical waveguides with position-dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of quasi-periodicity for small number of lattice sites. We obtain the Hofstadter butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserve the total intensity. •We show that PT symmetric Aubry–Andre model may have real spectrum.•We show that the reality of the spectrum depends sensitively on the degree of disorder.•We obtain the Hofstadter butterfly spectrum for PT symmetric Aubry–Andre model.•We discuss that phase transition from extended to localized states exists.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2014.05.005