Non-Hermitian physics
By Yuto Ashida, Z. Gong, Masahito Ueda. Advances in Physics, 2020
1,912 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0736f24022425837b954a6c02fabb7d76b4f47d5
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Citations in the corpus
- Chiral control of quantum states in non-Hermitian spin–orbit-coupled fermions (2021, background): “Furthermore, the possibility of exploring non-equilibrium dynamics, quantum thermodynamics [44] and information criticality [45] across thePT symmetry-breaking transition by engineering the non-Hermitian Hamiltonian in a dynamic manner is conceivable.”
- Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition (2020, background): “These issues could be addressed by relying on recent developments in Markovian open quantum many-body systems [178, 179].”