Non-Hermitian physics
2020/07/02 by Yuto Ashida, Zongping Gong, Masahito Ueda · 219 citations
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · doi:10.1080/00018732.2021.1876991
openalex created_date 2020/06/12 · openalex publication_date 2020/07/02 · openalex updated_date 2026/07/31
Abstract
A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity, and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, and acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena and subjects in quantum regimes, such as quantum resonances, superradiance, the continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, first given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.
Citations
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- Persistent Charge and Spin Currents in a Ferromagnetic Hatano-Nelson Ring
- Interacting many-body non-Hermitian systems as Markov chains
- Dynamically encircling an exceptional point through phase-tracked closed-loop control
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- Impact of noise on nonlinear-exceptional-point-based sensors
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- Non-Hermitian superconducting diode effect
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- Lyapunov formulation of band theory for disordered non-Hermitian systems
- Lindbladian versus Postselected Non-Hermitian Topology
- Sensitivity and Topology of Exceptional Rings in Nonlinear Non-Hermitian Planar Optical Microcavities
- Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
- Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
- Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
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