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We establish new results on the spectra and pseudo-spectra of tridiagonal $k$-Toeplitz operators and matrices. In particular, we prove the connection between the winding number of the eigenvalues of the symbol function and the exponential…

Mathematical Physics · Physics 2024-01-24 Habib Ammari , Silvio Barandun , Yannick De Bruijn , Ping Liu , Clemens Thalhammer

The non Hermitian skin effect, where bulk states accumulate at system boundaries, challenges the conventional bulk boundary correspondence. Here we propose a scheme to realize hybrid skin topological states in exciton polariton honeycomb…

Mesoscale and Nanoscale Physics · Physics 2025-12-02 Ruiqi Bao , R. Banerjee , S. Mandal , Huawen Xu , Shiji Li , Junfeng Gao , Timothy C. H. Liew

Anderson (localization) transition is a universal wave phenomenon characterized by a disorder-induced quantum phase transition from extended to localized states, whereas the non-Hermitian skin effect is a generic feature of non-Hermitian…

Disordered Systems and Neural Networks · Physics 2026-03-31 C. Wang , X. R. Wang , Hechen Ren

We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two interpretations of non-Hermitian topology: quantum…

Mesoscale and Nanoscale Physics · Physics 2021-02-24 Nobuyuki Okuma , Masatoshi Sato

Non-Hermitian lattices under semi-infinite boundary conditions sustain an extensive number of exponentially-localized states, dubbed non-Hermitian skin modes. Such states can be predicted from the nontrivial topology of the energy spectrum…

Quantum Physics · Physics 2022-07-26 Stefano Longhi

Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well-established for single-particle systems, but their proper characterization for general systems is…

Quantum Physics · Physics 2024-10-01 Kenji Shimomura , Masatoshi Sato

We demonstrate that dislocations in two-dimensional non-Hermitian systems can give rise to density accumulation or depletion through the localization of an extensive number of states. These effects are shown by numerical simulations in a…

Mesoscale and Nanoscale Physics · Physics 2021-12-16 Balaganchi A. Bhargava , Ion Cosma Fulga , Jeroen van den Brink , Ali G. Moghaddam

Recently, topological quantum states of non-Hermitian systems, exhibiting rich new exotic states, have attracted great attention in condensed-matter physics. As for the demonstration, most of non-Hermitian topological phenomena previously…

Mesoscale and Nanoscale Physics · Physics 2019-02-15 Huaiqiang Wang , Jiawei Ruan , Haijun Zhang

We demonstrate how the relative phase between the multiple time periodic driving can decide the emergence and the favorable localization direction of non-Hermitian skin modes. For the static non-Hermitian quantum chain with parity time…

Quantum Physics · Physics 2026-05-22 Huan-Yu Wang

The investigations of the spectral and dynamical delocalization-localization (DL) transition have revealed intriguing features in a wide range of non-Hermitian systems. The present study aims at exploring the spectral and dynamical…

Disordered Systems and Neural Networks · Physics 2023-03-08 Aditi Chakrabarty , Sanjoy Datta

Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian…

Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an exponential sensitivity to boundary conditions and an extensive number of edge-localized states in systems with open boundaries, a phenomena dubbed the…

Disordered Systems and Neural Networks · Physics 2021-04-14 Jahan Claes , Taylor L. Hughes

Recently, it was established that there exists a direct relation between the non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, and boundary zero modes for Hermitian topological…

Mesoscale and Nanoscale Physics · Physics 2020-07-10 Nobuyuki Okuma , Masatoshi Sato

Lattice models featuring the non-Hermitian skin effect have attracted rapidly growing interest due to their nontrivial spectral topology and the exotic field dynamics they enable. Such non-Hermitian lattices provide a promising paradigm for…

Quantum Physics · Physics 2025-02-19 Lei Du , Anton Frisk Kockum

The non-Hermitian skin effect can arise in materials that have asymmetric hoppings between atoms or resonating units, which makes the bulk eigenspectrum sensitive to boundary conditions. When skin effect emerges, eigenstates in the bulk…

Mesoscale and Nanoscale Physics · Physics 2022-02-21 Yi-Xin Xiao , C. T. Chan

The non-Hermitian skin effect, i.e. eigenstate condensation at the edges in lattices with open boundaries, is an exotic manifestation of non-Hermitian systems. In Bloch theory, an effective non-Hermitian Hamiltonian is generally used to…

Quantum Physics · Physics 2020-12-15 Stefano Longhi

The complex eigenenergies and non-orthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional…

Quantum Physics · Physics 2025-12-19 Jung-Wan Ryu , Jae-Ho Han , Chang-Hwan Yi , Hee Chul Park , Moon Jip Park

One of unique features of non-Hermitian systems is the extreme sensitive to their boundary conditions, e.g., the emergence of non-Hermitian skin effect (NHSE) under the open boundary conditions, where most of bulk states become localized at…

Disordered Systems and Neural Networks · Physics 2025-01-16 Hao Wang , Jin Liu , Tao Liu , Wen-Bo Ju

The non-Hermitian skin effect (NHSE) has been intensely investigated over the past few years and has unveiled new topological phases, which have no counterparts in Hermitian systems. Here we consider the hybridization between the NHSE in an…

Mesoscale and Nanoscale Physics · Physics 2024-02-13 Ruiqi Bao , Huawen Xu , Wouter Verstraelen , Timothy C. H. Liew

The pursuit of the non-Hermitian skin effect (NHSE) in various physical systems is of great research interest. Compared with recent progress in non-electronic systems, the implementation of the NHSE in condensed matter physics remains…

Mesoscale and Nanoscale Physics · Physics 2023-01-23 H. Geng , J. Y. Wei , M. H. Zou , L. Sheng , Wei Chen , D. Y. Xing
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