The duality of left and right eigenvectors underpins the comprehensive understanding of many physical phenomena.In Hermitian systems,left and right eigenvectors are simply Hermitian-conjugate pairs.In contrast,non-Her...The duality of left and right eigenvectors underpins the comprehensive understanding of many physical phenomena.In Hermitian systems,left and right eigenvectors are simply Hermitian-conjugate pairs.In contrast,non-Hermitian eigenstates have left and right eigenvectors that are distinct from each other.However,despite the tremendous interest in non-Hermitian physics in recent years,the roles of non-Hermitian left eigenvectors(LEVs)are still inadequately explored.Their physical consequences and observable effects remain elusive,so much so that LEVs seem largely like objects of primarily mathematical purpose.In this study,we present a method based on the non-Hermitian Green’s function for directly retrieving both LEVs and right eigenvectors(REVs)from experimentally measured steady-state responses.We validate the effectiveness of this approach in two separate acoustic experiments:one characterizes the non-Hermitian Berry phase,and the other measures extended topological modes.Our results not only unambiguously demonstrate observable effects related to non-Hermitian LEVs but also highlight the under-appreciated role of LEVs in non-Hermitian phenomena.展开更多
In this paper, the authors investigate the synchronization of an array of linearly coupled identical dynamical systems with a delayed coupling. Here the coupling matrix can be asymmetric and reducible. Some criteria e...In this paper, the authors investigate the synchronization of an array of linearly coupled identical dynamical systems with a delayed coupling. Here the coupling matrix can be asymmetric and reducible. Some criteria ensuring delay-independent and delay- dependent global synchronization are derived respectively. It is shown that if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronization stability of the network will be restrained, even eventually de-synchronized.展开更多
基金supported by the National Key R&D Program(No.2022YFA1404400)the Hong Kong Research Grants Council(Nos.RFS2223-2S01 and 12301822)the Hong Kong Baptist University(Nos.RC-RSRG/23-24/SCI/01 and RC-SFCRG/23-24/R2/SCI/12).
文摘The duality of left and right eigenvectors underpins the comprehensive understanding of many physical phenomena.In Hermitian systems,left and right eigenvectors are simply Hermitian-conjugate pairs.In contrast,non-Hermitian eigenstates have left and right eigenvectors that are distinct from each other.However,despite the tremendous interest in non-Hermitian physics in recent years,the roles of non-Hermitian left eigenvectors(LEVs)are still inadequately explored.Their physical consequences and observable effects remain elusive,so much so that LEVs seem largely like objects of primarily mathematical purpose.In this study,we present a method based on the non-Hermitian Green’s function for directly retrieving both LEVs and right eigenvectors(REVs)from experimentally measured steady-state responses.We validate the effectiveness of this approach in two separate acoustic experiments:one characterizes the non-Hermitian Berry phase,and the other measures extended topological modes.Our results not only unambiguously demonstrate observable effects related to non-Hermitian LEVs but also highlight the under-appreciated role of LEVs in non-Hermitian phenomena.
基金Project supported by the National Natural Science Poundation of China(Nos.60574044,60774074)the Graduate Student Innovation Fonndation of Fudan University.
文摘In this paper, the authors investigate the synchronization of an array of linearly coupled identical dynamical systems with a delayed coupling. Here the coupling matrix can be asymmetric and reducible. Some criteria ensuring delay-independent and delay- dependent global synchronization are derived respectively. It is shown that if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronization stability of the network will be restrained, even eventually de-synchronized.
