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.
Symme- try and topology in non-Hermitian physics,
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In clean multiband non-Hermitian systems the skin effect is independent of point-gap winding; topology lives in the Toeplitz index and singular-value spectrum, not the eigenspectrum.
In a non-Hermitian skyrmion, the right-state charge is homotopy-protected while the biorthogonal charge loses quantization at a real-space exceptional ring on the equator.
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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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
In clean multiband non-Hermitian systems the skin effect is independent of point-gap winding; topology lives in the Toeplitz index and singular-value spectrum, not the eigenspectrum.
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A real-space exceptional ring mediates an eigenframe-charge transition in a non-Hermitian skyrmion
In a non-Hermitian skyrmion, the right-state charge is homotopy-protected while the biorthogonal charge loses quantization at a real-space exceptional ring on the equator.
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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.