2025/10/06 by P. Schmelcher, Diakonos, Fotis K., Schmelcher, P.
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Photonic Systems #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #Quasicrystal Structures and Properties #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2510.04518
openalex publication_date 2025/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Isospectrally patterned lattices (IPL) have recently been shown to exhibit a rich band structure comprising both regimes of localized as well as extended states. The localized states show a single center localization behaviour with a characteristic localization length. We derive a continuum analogue of the IPL which allows us to determine analytically its eigenvalue spectrum and eigenstates thereby obtaining an expression for the localization length which involves the ratio of the coupling among the cells of the lattice and the phase gradient across the lattice. This continuum model breaks chiral symmetry but still shows a pairing of partner states with positive and negative energies except for the ground state. We perform a corresponding symmetry analysis which illuminates the continuum models structure as compared to a corresponding chirally symmetric Hamiltonian.