Non-Hermitian physics

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 delinea...

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Vydáno v:Advances in physics Ročník 69; číslo 3; s. 249 - 435
Hlavní autoři: Ashida, Yuto, Gong, Zongping, Ueda, Masahito
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 02.07.2020
Taylor & Francis Ltd
Témata:
Acoustics
bulk-edge correspondence
Critical phenomena
dissipation
edge modes
electrical circuits
Energy transfer
Linear algebra
mechanics
Non-Hermitian systems
nonreciprocal transport
nonunitary dynamics
Nuclear physics
open quantum systems
photonics
Physics
quantum many-body physics
quantum optics
quantum walk
topological invariants
Topology
ISSN:0001-8732, 1460-6976
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Shrnutí: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.
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ISSN:0001-8732
1460-6976
DOI:10.1080/00018732.2021.1876991