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Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…

Quantum Physics · Physics 2007-05-23 A. J. Scott , G. J. Milburn

Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena, ranging from photonics and atomic and molecular systems to nuclear physics and mesoscopic electronic systems. An important question…

Mesoscale and Nanoscale Physics · Physics 2021-04-21 Ygor Pará , Giandomenico Palumbo , Tommaso Macrì

In recent years, non-Hermitian quantum physics has gained a lot in popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner…

Quantum Physics · Physics 2022-09-09 Jake Southall , Daniel Hodgson , Robert Purdy , Almut Beige

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in…

Mesoscale and Nanoscale Physics · Physics 2023-03-29 Nobuyuki Okuma , Masatoshi Sato

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…

Statistical Mechanics · Physics 2023-12-04 Kui Cao , Su-Peng Kou

During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…

We report the propagation of fast wavepackets in classical non-Hermitian lattices, where the group velocity is controlled by the non-Hermiticity parameters, and can be made higher than in the Hermitian counterpart. Specifically, we obtain a…

Mesoscale and Nanoscale Physics · Physics 2024-07-16 Yehonatan Benisty , Sayan Jana , Lea Sirota

Although non-Hermitian dynamics near exceptional points (EPs) provide a route to accelerated entanglement generation, entanglement can also be generated far from EPs at comparable or even higher rates. However, the behavior of such…

Quantum Physics · Physics 2026-04-21 Hamid Sakhouf , Peng Xue

Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…

Optics · Physics 2025-01-23 Jianming Wen , Xiaoshun Jiang , Liang Jiang , Min Xiao

Altermagnets are rapidly emerging as a highly promising platform for spintronics, yet dynamically controlling their spin responses remains a fundamental challenge. In this work, we demonstrate that introducing periodic optical driving and…

Mesoscale and Nanoscale Physics · Physics 2026-05-18 Kai Chen , Jie Zhu

Non-Hermitian systems enable continuous and smooth tuning of topological phases through externally controllable loss/gain parameters. Without altering the intrinsic lattice structure, merely fine-tuning the intensity or spatial distribution…

Applied Physics · Physics 2026-03-11 Shuanghuizhi Li , Bowei Wu , Tingfeng Ma , Jiaqi Zhang , Chenbowen Lou

Topological winding in non-Hermitian systems are generally associated to the Bloch band properties of lattice Hamiltonians. However, in certain non-Hermitian models topological winding naturally arise from the dynamical evolution of the…

Optics · Physics 2025-04-10 Stefano Longhi

Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…

Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are $\mathcal{PT}$-symmetric. These exhibit exceptional points (EPs) where the eigenspectrum changes from purely real to purely imaginary…

Quantum Physics · Physics 2025-06-23 Jia-Jia Wang , Yu-Hong He , Chang-Geng Liao , Rong-Xin Chen , Jacob A. Dunningham

Kinetically constrained models have been widely studied in the context of glass formers and non-equilibrium statistical mechanics. Although their simple local rules often result in structureless static properties, their dynamics exhibit…

Quantum Physics · Physics 2026-03-20 Marcel Cech , Johan du Buisson , Cecilia De Fazio , Federico Carollo , Igor Lesanovsky

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the…

Quantum Physics · Physics 2016-06-07 E M Graefe , H J Korsch , A Rush

By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…

Quantum Physics · Physics 2017-10-03 Barbara Drossel

The complex energy bands of non-Hermitian systems braid in momentum space even in one dimension. Here, we reveal that the non-Hermitian braiding underlies the Hermitian topological physics with chiral symmetry under a general framework that…

Mesoscale and Nanoscale Physics · Physics 2023-10-09 W. B. Rui , Y. X. Zhao , Z. D. Wang

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane…

The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…

Quantum Physics · Physics 2024-01-26 Gerard McCaul , Dmitry V. Zhdanov , Denys I. Bondar