Speaker
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I report on three different expansion approaches that systematically capture spatial and dynamical content of complex wave functions.
The first approach uses the surface Green's function to analyze and design interface and defect states at any arbitrary energy [1].
The second approach expands the dynamical correlations of generalized spectral form factors in ergodic stochastic systems [2,3].
The third approach expands the resolvent Green's function in terms of modes of the adjugate matrix, which provides detailed insights into spectral deficient scenarios [4,5,6].
[1] Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces, H. Schomerus, Phys. Rev. Res 5, 043224 (2023).
[2] Hierarchical analytical approach to universal spectral correlations in Brownian quantum chaos, T. Kalsi, A. Romito, and H. Schomerus, Phys. Rev. B 111, 094211 (2025).
[3] Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling, T. Kalsi, A. Romito, and H. Schomerus, Quantum 9, arXiv:2310.11355 (2025).
[4] Eigenvalue sensitivity from eigenstate geometry near and beyond arbitrary-order exceptional points, H. Schomerus, Phys. Rev. Res. 6, 013044 (2024).
[5] Fragmented exceptional points and their bulk and edge realizations in lattice models, S. Bid and H. Schomerus, Phys. Rev. B 112, 195433 (2025).
[6] Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point, S. Bid and H. Schomerus, Phys. Rev. Res. 7, 023062 (2025).