Non-Hermitian skyrmions carry two topological charges that coincide in the Hermitian limit but one breaks down at exceptional points where the biorthogonal Bloch field diverges.
Symme- try and topology in non-Hermitian physics,
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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.
The non-Hermitian skin effect originates from spectral instability and non-reciprocity instead of point-gap winding of the Bloch Hamiltonian.
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.
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.
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Exceptional Points as Manifestations of Topological-Charge Breakdown in a Non-Hermitian Skyrmion
Non-Hermitian skyrmions carry two topological charges that coincide in the Hermitian limit but one breaks down at exceptional points where the biorthogonal Bloch field diverges.
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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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Pseudospectral phenomena and the origin of the non-Hermitian skin effect
The non-Hermitian skin effect originates from spectral instability and non-reciprocity instead of point-gap winding of the Bloch Hamiltonian.
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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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Quantum chaotic systems: a random-matrix approach
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.