191 pages https://arxiv.org/pdf/2006.01837.pdf Table 1. A wide variety of classical and quantum systems described by non-Hermitian matrices/operators together with their physical origins of non-Hermiticity, presented in order of appearance in the present review. Systems / Processes Physical origin of non-Hermiticity Theoretical methods Photonics / Gain and loss of photons / Maxwell equations [12, 13] Mechanics / Friction / Newton equation [14, 15] Electrical circuits / Joule heating / Circuit equation [16] Stochastic processes / Nonreciprocity of state transitions / Fokker-Planck equation [17, 18] Soft matter and fluid / Nonlinear instability / Linearized hydrodynamics [19–21] Nuclear reactions / Radiative decays / Projection methods [4–6] Mesoscopic systems / Finite lifetimes of resonances / Scattering theory [22, 23] Open quantum systems / Dissipation / Master equation [24, 25] Quantum measurement / Measurement backaction / Quantum trajectory approach [26–31]

191 pages
Table 1. A wide variety of classical and quantum systems described by non-Hermitian matrices/operators together with their
physical origins of non-Hermiticity, presented in order of appearance in the present review.
Systems / Processes Physical origin of non-Hermiticity Theoretical methods
Photonics / Gain and loss of photons / Maxwell equations [12, 13]
Mechanics / Friction / Newton equation [14, 15]
Electrical circuits / Joule heating / Circuit equation [16]
Stochastic processes / Nonreciprocity of state transitions / Fokker-Planck equation [17, 18]
Soft matter and fluid / Nonlinear instability / Linearized hydrodynamics [19–21]
Nuclear reactions / Radiative decays / Projection methods [4–6]
Mesoscopic systems / Finite lifetimes of resonances / Scattering theory [22, 23]
Open quantum systems / Dissipation / Master equation [24, 25]
Quantum measurement / Measurement backaction / Quantum trajectory approach [26–31]

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