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The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…

Quantum Physics · Physics 2025-11-27 Pengfei Lu , Yang Liu , Qifeng Lao , Teng Liu , Xinxin Rao , Ji Bian , Hao Wu , Feng Zhu , Le Luo

Non-Hermitian photonic lattices combine the peculiar consequences of energy non-conservation with the physics of bandstructures, giving rise to a variety of exotic properties not found in conventional materials or photonic metamaterials. In…

Optics · Physics 2023-05-17 Qiang Wang , Y. D. Chong

Non-Hermitian models describe the physics of ubiquitous open systems with gain and loss. One intriguing aspect of non-Hermitian models is their inherent topology that can produce intriguing boundary phenomena like resilient higher-order…

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…

Mesoscale and Nanoscale Physics · Physics 2019-01-21 V. M. Martinez Alvarez , J. E. Barrios Vargas , M. Berdakin , L. E. F. Foa Torres

We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D…

Soft Condensed Matter · Physics 2020-05-19 Di Zhou , Junyi Zhang

Exploring the deep insights into localization, disorder, and wave transport in non-Hermitian systems is an emergent area of research of relevance in different areas of physics. Engineered photonic lattices, with spatial regions of optical…

Optics · Physics 2025-04-10 Stefano Longhi

Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled…

Mesoscale and Nanoscale Physics · Physics 2018-03-20 L. Jin

Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of…

Mesoscale and Nanoscale Physics · Physics 2020-03-17 Longwen Zhou

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in…

Mesoscale and Nanoscale Physics · Physics 2019-07-18 Ananya Ghatak , Tanmoy Das

Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which…

Mesoscale and Nanoscale Physics · Physics 2016-05-26 Mark S. Rudner , Michael Levin , Leonid S. Levitov

We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is…

Quantum Physics · Physics 2016-04-04 Tony E. Lee

Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…

Mesoscale and Nanoscale Physics · Physics 2018-09-25 Zongping Gong , Yuto Ashida , Kohei Kawabata , Kazuaki Takasan , Sho Higashikawa , Masahito Ueda

In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a…

Statistical Mechanics · Physics 2018-08-29 Longwen Zhou , Qing-hai Wang , Hailong Wang , Jiangbin Gong

Nonlinear topological photonics is an emerging field aiming at extending the fascinating properties of topological states to the realm where interactions between the system constituents cannot be neglected. Interactions can indeed trigger…

In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies of…

Quantum Physics · Physics 2022-07-26 Stefano Longhi

The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$ non-Hermitian…

Quantum Gases · Physics 2020-08-26 Xingran Xu , Haodi Liu , Zhidong Zhang , Zhaoxin Liang

Non-Hermitian topological matter provides a platform for engineering phenomena that go beyond the capabilities of Hermitian systems, enabling the use of losses to engineer topological phenomena. Non-Hermitian models often rely on artificial…

Optical superlattices with sublattice symmetry subjected to a synthetic imaginary gauge field undergo a topological phase transition in the Bloch energy spectrum, characterized by the change of a spectral winding number. For a narrow gap,…

Optics · Physics 2021-09-06 Stefano Longhi

Solids built out of active components can exhibit non-reciprocal elastic coefficients that give rise to non-Hermitian wave phenomena. Here, we investigate non-Hermitian effects present at the boundary of two-dimensional active elastic media…

Soft Condensed Matter · Physics 2020-09-16 Colin Scheibner , William T. M. Irvine , Vincenzo Vitelli
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