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Embedded States in the Continuum for P T ‐Symmetric Systems
Author(s) -
Molina Mario I.,
Kivshar Yuri S.
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12058
Subject(s) - bounded function , hermitian matrix , lattice (music) , bound state , symmetry (geometry) , physics , symmetry breaking , theoretical physics , mathematics , pure mathematics , quantum mechanics , mathematical analysis , geometry , acoustics
We introduce the novel concept of a bound state in the continuum (BIC) for a binary lattice satisfying the P T ‐symmetry condition. We show how to build such state and the local potential necessary to sustain it. We find that an appropriate choice of the envelope function can bring the system from a P T ‐symmetric phase into a Hermitian one. For more general envelope functions, the BIC can still be created but the bounded state will force the system to undergo the P T ‐symmetry breaking transition.