Adiabatic theorem for non-Hermitian quantum systems with non-degenerate real eigenvalues: A proof following Kato's approach

Quantum Physics arXiv:2511.00968 (quant-ph) [Submitted on 2 Nov 2025] Title:Adiabatic theorem for non-Hermitian quantum systems with non-degenerate real eigenvalues: A proof following Kato's approach Authors:Minyi Huang, Ray-Kuang Lee View a PDF of the paper titled Adiabatic theorem for non-Hermitian quantum systems with non-degenerate real eigenvalues: A proof following Kato's approach, by Minyi Huang and 1 other authors View PDF HTML (experimental) Abstract:The adiabatic theorem is one of the most interesting and significant theorem in quantum mechanics. In 1950, T. Kato gave an elegant proof of this result [1]. However, the validation of adiabatic theorem for non-Hermitian quantum systems is unrevealed. In this paper, by following Kato' approach, we prove rigorously that the adiabatic theorem is still valid for non-Hermitian systems with non-degenerate real eigenvalues. Moreover, our proof utilizes the complex Berry phase, instead of the orthogonal projections used in Kato's work. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2511.00968 [quant-ph] (or arXiv:2511.00968v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.00968 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Minyi Huang [view email] [v1] Sun, 2 Nov 2025 15:16:21 UTC (11 KB) Full-text links: Access Paper: View a PDF of the paper titled Adiabatic theorem for non-Hermitian quantum systems with non-degenerate real eigenvalues: A proof following Kato's approach, by Minyi Huang and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)