A two-scale effective model for defect-induced localization transitions in non-Hermitian systems

2024/03/19 by Bryn Davies, S Barandun, Davies, Bryn +7 · 2 citations
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2403.12546

openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

We illuminate the fundamental mechanism responsible for the transition between the non-Hermitian skin effect and defect-induced localization in the bulk. We study a Hamiltonian with non-reciprocal couplings that exhibits the skin effect (the localization of all eigenvectors at one edge) and add an on-site defect in the center. Using a two-scale asymptotic method, we characterize the long-scale growth and decay of the eigenvectors and derive a simple and intuitive effective model for the transition that occurs when the defect is sufficiently large that one of the modes is localized at the defect site, rather than at the edge of the system.

Cited by

• Spectra and pseudospectra of non-Hermitian Toeplitz operators: Eigenvector decay transitions in banded and dense matrices
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder

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