A Widom determinant expansion reveals that finite-size edge states in non-Hermitian chains can be absorbed by the bulk spectrum at a critical system size due to competition between boundary-projected Green's function subsets.
Exceptional topology of non-Hermitian systems
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits,s and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.
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Imaginary magnetic fields induce exceptional points in neutral meson mass spectra computed via hadronic effective Lagrangian and constituent quark models, separating real and complex eigenvalue regimes.
For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.
An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically relevant observable.
Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
A holographic toy model is constructed for third-order photonic exceptional points in ternary microrings, with numerical spectra, phase rigidity, and connections to the theta-vacuum of QCD via topological structures and a second-order EP in a perturbed model.
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Kubo-Martin-Schwinger conditions for non-Hermitian systems
For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
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A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.
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Exceptional Points and Resonance in Black Hole Ringdown
An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically relevant observable.
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Non-Hermitian Rayleigh-Schr\"{o}dinger-like Perturbation Theory at Exceptional Point
Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.
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Real-time pseudo entropy and modular-Hamiltonian correlations
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
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Photonic Exceptional Points in Holography and QCD
A holographic toy model is constructed for third-order photonic exceptional points in ternary microrings, with numerical spectra, phase rigidity, and connections to the theta-vacuum of QCD via topological structures and a second-order EP in a perturbed model.
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