Connections between the open-boundary spectrum and the generalized Brillouin zone in non-Hermitian systems
TLDR
In this paper , the authors connect the topological geometry of the open-boundary spectrum with the Brillouin zone (GBZ) and provide an efficient numerical method capable of calculating them accurately.Abstract:
Periodic-boundary spectrum, open-boundary spectrum, as well as the generalized Brillouin zone (GBZ) are three essential properties of a one-dimensional non-Hermitian system. In this paper we illustrate that the deep connections between them can be revealed by a series of special similar transformations. This viewpoint closely connects the topological geometry of the open-boundary spectrum with the GBZ and provides an efficient numerical method capable of calculating them accurately. We further extend these connections to non-Hermitian systems in the symplectic symmetry class. We show that if just the open-boundary features of a non-Hermitian system such as the spectrum and the GBZ, are concerned, the relevant symmetry we should consider is not that of the original system itself, but that of one that has higher symmetry and is related to the original system by a similarity transformation. read more
Citations
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Designing non-Hermitian real spectra through electrostatics.
TL;DR: In this paper , the diagonalization of non-Hermitian Hamiltonians is recast as a Poisson boundary value problem, and the electrostatics analogy is used to design new classes of parent Hamiltonians with real spectra.
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Self-Healing of Non-Hermitian Topological Skin Modes
TL;DR: In this paper , a unique feature of non-Hermitian (NH) systems is the NH skin effect, i.e., the edge localization of an extensive number of bulk-band eigenstates in a lattice with open or semi-infinite boundaries.
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Non-Hermitian skin effect and self-acceleration
TL;DR: In this article , self-acceleration of the wave function is demonstrated to occur rather generally in single-band lattice models probed by single-site excitation, where the acceleration turns out to be proportional to the area enclosed by the energy spectrum of the Bloch Hamiltonian under periodic boundary conditions.
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Filling up complex spectral regions through non-Hermitian disordered chains
TL;DR: In this article , the authors propose a simple and robust ansatz for constructing models whose eigenspectra fill up generic prescribed regions, using specially designed non-Hermitian random couplings that allow the coexistence of eigenstates with a continuum of localization lengths.
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Hybrid skin-topological modes without asymmetric couplings
TL;DR: In this article , the second-order non-Hermitian skin effect without asymmetric couplings is studied, where the bulk does not support a point gap but localization at the corner still occurs, and a generic route to hybrid skin-topological modes is further successfully extended to nonequilibrium topological systems with gain and loss.
References
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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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Observation of PT-Symmetry Breaking in Complex Optical Potentials
A. Guo,Gregory J. Salamo,David Duchesne,Roberto Morandotti,M. Volatier-Ravat,Vincent Aimez,Georgios A. Siviloglou,Demetrios N. Christodoulides +7 more
TL;DR: This work demonstrates experimentally passive PT-symmetry breaking within the realm of optics, which leads to a loss induced optical transparency in specially designed pseudo-Hermitian guiding potentials.
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Parity–time synthetic photonic lattices
Alois Regensburger,Christoph Bersch,Mohammad-Ali Miri,Georgy Onishchukov,Demetrios N. Christodoulides,Ulf Peschel +5 more
TL;DR: The experimental observation of light transport in large-scale temporal lattices that are parity–time symmetric is reported and it is demonstrated that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points.
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Unidirectional invisibility induced by PT-symmetric periodic structures.
Zin Lin,Hamidreza Ramezani,Toni Eichelkraut,Tsampikos Kottos,Hui Cao,Demetrios N. Christodoulides +5 more
TL;DR: Parity-time (PT) symmetric periodic structures, near the spontaneous PT-symmetry breaking point, can act as unidirectional invisible media and the transmission coefficient and phase are indistinguishable from those expected in the absence of a grating.
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Complex extension of quantum mechanics
TL;DR: If PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian, and this work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.