A diagonalization-free Krylov (bi-Lanczos/Arnoldi) construction yields exact or truncated adiabatic gauge potentials for non-Hermitian STA, reducing them to sparse matrix equations that suppress nonadiabatic excitations and detect PT/EP transitions.
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abstract
The adiabatic theorem is one of the most interesting and significant theorems in quantum mechanics. However, the adiabatic theorem can fail for general non-Hermitian quantum systems. In this paper, by utilizing the complex geometric phase, the functional calculus for biorthogonal systems and the Gr\"{o}nwall inequality, we prove rigorously that the adiabatic theorem is still valid for diagonalizable non-Hermitian systems with real eigenvalues. The proof also justifies the definition of a complex Berry phase for non-Hermitian systems, in both Abelian and non-Abelian cases.
years
2026 2representative citing papers
ResRank unifies retrieval and listwise reranking by compressing passages to one token each, using residual connections and cosine-similarity scoring, achieving competitive effectiveness on TREC DL and BEIR benchmarks with zero generated tokens.
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Shortcuts to Adiabaticity for non-Hermitian systems in Krylov Space
A diagonalization-free Krylov (bi-Lanczos/Arnoldi) construction yields exact or truncated adiabatic gauge potentials for non-Hermitian STA, reducing them to sparse matrix equations that suppress nonadiabatic excitations and detect PT/EP transitions.
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ResRank: Unifying Retrieval and Listwise Reranking via End-to-End Joint Training with Residual Passage Compression
ResRank unifies retrieval and listwise reranking by compressing passages to one token each, using residual connections and cosine-similarity scoring, achieving competitive effectiveness on TREC DL and BEIR benchmarks with zero generated tokens.