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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Published in:	Advances in physics Vol. 69; no. 3; pp. 249 - 435
Main Authors:	Ashida, Yuto, Gong, Zongping, Ueda, Masahito
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 02.07.2020 Taylor & Francis Ltd
Subjects:	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
Online Access:	Get full text
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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.
AbstractList	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.
Author	Ueda, Masahito Ashida, Yuto Gong, Zongping
Author_xml	– sequence: 1 givenname: Yuto surname: Ashida fullname: Ashida, Yuto email: ashida@phys.s.u-tokyo.ac.jp organization: University of Tokyo – sequence: 2 givenname: Zongping surname: Gong fullname: Gong, Zongping organization: Max-Planck-Institut für Quantenoptik – sequence: 3 givenname: Masahito surname: Ueda fullname: Ueda, Masahito organization: RIKEN Center for Emergent Matter Science (CEMS)
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Snippet	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...
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SubjectTerms	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
Title	Non-Hermitian physics
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