The physics of exceptional points

By W. Heiss. 2012

1,404 citations recorded by the source corpus.

A short résumé is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They are associated with symmetry breaking for -symmetric Hamiltonians, where a great number of experiments has been performed, in particular in optics, and to an increasing extent in atomic and molecular physics. EPs are involved in quantum phase transition and quantum chaos; they produce dramatic effects in multichannel scattering, specific time dependence and more. In nuclear physics, they are associated with instabilities and continuum problems. Being spectral singularities they also affect approximation schemes. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1557bf0460901c6b5ecdea90b64f042bc72eb92a

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Unidirectional reflectionless light propagation at exceptional points (2017, background): “EPs have been studied in lasers [5], coupled dissipative dynamical systems [6], mechanics [7], electronic circuits [8], gyrokinetics of plasmas [9], and atomic as well as molecular systems [10].”
Topological active matter (2020, background): “The extreme limit of this failure occurs when two (or more) eigenvectors become collinear: this is called an exceptional point 229 .”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “Non-Hermitian matrices exhibit unconventional characteristics compared with Hermitian ones [35]: eigenstates are, in general, nonorthogonal [36], and a complex-energy spectrum can possess exceptional points [37,38].”
Exceptional points in optics and photonics (2019, background): “The best example of such deviation is the emergence of singularities, so-called exceptional points, at which two or more eigenvalues, and their associated eigenvectors, simultaneously coalesce and become degenerate (5).”
Dynamically Encircling Exceptional Points: In situ Control of Encircling Loops and the Role of the Starting Point (2018, background): “INTRODUCTION Exceptional points (EPs) are degeneracies in nonHermitian systems [1-4].”
Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points (2017, background): “Depending on the EP’s chirality [21, 49], the zero energy state turns out to be localized on one edge or the opposite.”