Topological enhancement of non-normality in non-Hermitian skin effects

Fuente: arXiv
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Hauptverfasser: Nakai, Yusuke O., Okuma, Nobuyuki, Nakamura, Daichi, Shimomura, Kenji, Sato, Masatoshi
Format: Preprint
Veröffentlicht: 2023
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author Nakai, Yusuke O.
Okuma, Nobuyuki
Nakamura, Daichi
Shimomura, Kenji
Sato, Masatoshi
author_facet Nakai, Yusuke O.
Okuma, Nobuyuki
Nakamura, Daichi
Shimomura, Kenji
Sato, Masatoshi
contents The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.
format Preprint
id arxiv_https___arxiv_org_abs_2304_06689
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Topological enhancement of non-normality in non-Hermitian skin effects
Nakai, Yusuke O.
Okuma, Nobuyuki
Nakamura, Daichi
Shimomura, Kenji
Sato, Masatoshi
Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Statistical Mechanics
Optics
Quantum Physics
The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.
title Topological enhancement of non-normality in non-Hermitian skin effects
topic Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Statistical Mechanics
Optics
Quantum Physics
url https://arxiv.org/abs/2304.06689