Exceptional points of non-Hermitian operators
By W. Heiss. 2003
516 citations recorded by the source corpus.
Exceptional points associated with non-Hermitian operators, i.e. operators being non-Hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within the domain of real parameters the exceptional points are the points where eigenvalues switch from real to complex values. These and other results are exemplified by a classical problem leading to exceptional points of a non-Hermitian matrix.
Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/369c5b1aef867f57cd2fb82b697b977b618aa93a
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In Atomic and Molecular Physics, and Optics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Exceptional points in optics and photonics (2019, background): “The physical importance of exceptional points was pointed out in earlyworks (7,8), inwhich the terminology of nonHermitian degeneracy was used to distinguish such critical points from regular degeneracies occurring in Hermitian systems (9, 10).”
- Experimental realization of a Weyl exceptional ring (2018, background): “This enables photonic systems to realize phenomena exclusive to non-Hermitian systems, such as exceptional points, a class of degeneracies where two or more eigenvalues and their associated eigenvectors coalesce, and the system possesses a non-trivial Jordan block form [33, 34].”
- Loss-induced suppression and revival of lasing (2014, background): “g the parameters of such a system, its dissipative complex eigenvalues and the corresponding eigenstates may coalesce, giving rise to a non-Hermitian degeneracy, also called an Exceptional Point (EP) (4). The presence of such anEP has a dramatic effect on the system, leading to nontrivial physics wi”
- Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system (2018, background): “In contrast to level degeneracy points in Hermitian systems, the EP is associated with level coalescence, in which not only the eigenenergies but also the eigenstates become identical [12, 13].”
- Unidirectional reflectionless light propagation at exceptional points (2017, methodology): “Unlike the Hermitian case, the levels approach each other in the form of a cusp rather than a smooth approach because of the plain square-root behavior of the singularity (Figure 9C) [1, 4].”