Non-hermitian quantum mechanics

By E. Brändas. 2012

921 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/8170b635d89255f81d8368dc1b8cca3b87a7d4ae

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Loss-induced suppression and revival of lasing (2014, background): “final many-body wave functions, and is referred to as Fermi-edge singularity (3).”
Unidirectional reflectionless light propagation at exceptional points (2017, background): “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].”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “Non-Hermitian matrices exhibit unconventional characteristics compared with Hermitian ones [32]: eigenstates are, in general, nonorthogonal [33] and a complex-energy spectrum can possess exceptional points [34, 35].”
General description of quasiadiabatic dynamical phenomena near exceptional points (2014, background): “(3) more compactly as ̇x = −iM x, where x is the state vector and M is the dynamical matrix, or sometimes called in this context a non-Hermitian Hamiltonian [9], i.e., x := ( α1 α2 ) , M := (−ω − iγ /2 g g ω + iγ /2 ) .”
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems. (2016, background): “NonHermitian systems, however, exhibit a distinct class of spectral degeneracies known as exceptional points (EPs), which are branch points in a 2D parameter space where the Hamiltonian becomes non-diagonalizable [4, 9, 10].”
Dynamically encircling an exceptional point for asymmetric mode switching (2016, background): “( ) V x y , , which leaves the validity of equations (3) and (4) intact.”
Quasiprobability behind the out-of-time-ordered correlator (2017, background): “Additionally, since ρ ′ is nonHermitian, non-Hermitian quantum mechanics might offer insights [133].”
Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points (2017, background): “Indeed, close to an EP two measures of non-Hermiticity, the Hamiltonian’s defectiveness and the biorthogonality of its left and right eigenstates [39], are typically very fragile, e.”
Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system (2018, background): “Extending physical parameters from the real axis to the complex plane largely deepens our understanding of quantum mechanics [1, 2] and enriches our controllability of quantum systems [3–11].”
The Quantum Harmonic Otto Cycle (2016, background): “Their product is equal to zero, showing that the eigenvector is self-orthogonal [104].”
Recent development of complex scaling method for many-body resonances and continua in light nuclei (2014, methodology): “The detailed of this method is explained in the review given by Moiseyev [9].”