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arXiv · 2607.19737

The Quantum Adiabatic Theorem for Non-Hermitian Dynamics

G. M. V. S. Aponso·B. P. W. Fernando·K. K. W. A. S. Kumara·R. P. K. De Silva
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Abstract

We establish a quantitative adiabatic estimate for a class of finite-dimensional non-Hermitian Schr\"odinger dynamics. The original non-Hermitian Hamiltonian is assumed to be diagonalizable with real spectrum and non-crossing eigenvalues. We then construct a dynamically compatible time-dependent metric operator, and its positive square root defines a Dyson map. The associated Dyson-transformed Hamiltonian is Hermitian. When this Dyson-transformed Hamiltonian satisfies the Hermitian adiabatic assumption, the standard resolvent-projection method gives an explicit adiabatic estimate in the Hermitian representation. Pulling this estimate back through the Dyson map gives an approximation in the original non-Hermitian representation. The resulting Dyson-pulled-back projections are then compared with the spectral projections of the original non-Hermitian Hamiltonian by using a contour-resolvent estimate. The final bound contains two contributions: the pulled-back Hermitian adiabatic error and the projection-comparison error. A two-level non-Hermitian model is presented to illustrate the hypotheses of the theorem and the two contributions appearing in the final estimate.

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G. M. V. S. Aponso, B. P. W. Fernando, K. K. W. A. S. Kumara, R. P. K. De Silva. 2026-07-22. The Quantum Adiabatic Theorem for Non-Hermitian Dynamics. https://arxiv.org/abs/2607.19737

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