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.

Yuto Ashida

Zongping Gong

Masahito Ueda

Advances in Physics

ADVANCES IN PHYSICS 发表专家对凝聚态物理学家感兴趣和重要的主题的权威评论。它适用于对期刊领域有基本知识的积极读者，旨在从作者的角度引出所审查主题的要点。该期刊的范围包括凝聚态物理和统计力学：广义上包括与量子信息、冷原子、软物质物理和生物物理学的重叠。读者群：大学、工业和研究机构的物理学家、材料科学家和物理化学家。

The journal "Advances in Physics" publishes authoritative reviews on important topics of interest to condensed matter physicists. It is aimed at actively engaged readers who possess a fundamental understanding of the field, providing insights from the authors' perspectives. The scope of the journal includes condensed matter physics and statistical mechanics, broadly encompassing overlaps with quantum information, cold atoms, soft matter physics, and biophysics. The readership primarily consists of physicists, materials scientists, and physical chemists from universities, industry, and research institutions.

《Advances in Physics》期刊发表关于凝聚态物理学领域重要主题的权威评论，旨在为具备基本知识的读者提供深入的见解。期刊内容涵盖凝聚态物理和统计力学，广泛涉及量子信息、冷原子、软物质物理和生物物理学等交叉领域。其读者群体主要包括大学、工业界和研究机构的物理学家、材料科学家以及物理化学家。

Category	Quartile
物理与天体物理	1
物理与天体物理, 物理凝聚态物理	1

Non-Hermitian physics

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info

Category	Quartile
PHYSICS, CONDENSED MATTER	1