Nonlinear waves in PT -symmetric systems
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TLDR
The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra as discussed by the authors, which has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc.Abstract:
The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra. The concept has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc. The inclusion of nonlinearity has led to a number of new phenomena for which no counterparts exist in traditional dissipative systems. Several examples of nonlinear parity-time symmetric systems in different physical disciplines are presented and their implications discussed.read more
Citations
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Journal ArticleDOI
Non-Hermitian physics and PT symmetry
Ramy El-Ganainy,Konstantinos G. Makris,Mercedeh Khajavikhan,Ziad H. Musslimani,Stefan Rotter,Demetrios N. Christodoulides +5 more
TL;DR: In this paper, the interplay between parity-time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics has been explored both theoretically and experimentally.
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Exceptional points in optics and photonics.
TL;DR: The topic of exceptional points in photonics is reviewed and some of the possible exotic behavior that might be expected from engineering such systems are explored, as well as new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements.
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Parity-time symmetry and exceptional points in photonics.
TL;DR: The role of PT symmetry and non-Hermitian dynamics for synthesizing and controlling the flow of light in optical structures is highlighted and a roadmap for future studies and potential applications is provided.
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Topological phases of non-Hermitian systems
Zongping Gong,Yuto Ashida,Kohei Kawabata,Kazuaki Takasan,Sho Higashikawa,Masahito Ueda,Masahito Ueda +6 more
TL;DR: In this article, a coherent framework of topological phases of non-Hermitian Hamiltonians was developed, and the K-theory was applied to systematically classify all the topology phases in the Altland-Zirnbauer classes in all dimensions.
Journal ArticleDOI
Topological Phases of Non-Hermitian Systems
Zongping Gong,Yuto Ashida,Kohei Kawabata,Kazuaki Takasan,Sho Higashikawa,Masahito Ueda,Masahito Ueda +6 more
TL;DR: In this paper, a coherent framework of topological phases of non-Hermitian Hamiltonians was developed, and the K-theory was applied to systematically classify all the topology phases in the Altland-Zirnbauer classes in all dimensions.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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Controlling Electromagnetic Fields
TL;DR: This work shows how electromagnetic fields can be redirected at will and proposes a design strategy that has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.
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Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
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Metamaterials and negative refractive index.
TL;DR: Recent advances in metamaterials research are described and the potential that these materials may hold for realizing new and seemingly exotic electromagnetic phenomena is discussed.