Geometric Instability and Self-Limitation in Driven Quantum Systems
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Quantum Physics arXiv:2606.00259 (quant-ph) [Submitted on 29 May 2026] Title:Geometric Instability and Self-Limitation in Driven Quantum Systems Authors:A.M.Tishin View a PDF of the paper titled Geometric Instability and Self-Limitation in Driven Quantum Systems, by A.M.Tishin View PDF Abstract:We develop a unified geometric framework for local non-adiabaticity in driven quantum systems. We show that the previously introduced AMT non adiabaticity parameter arises as a special realization of a more general geometric instability criterion governed by the normalized Fubini Study distinguishability speed. The local geometric evolution speed is identified as the physically relevant quantity controlling the onset of non-adiabatic instability. We introduce a universal dimensionless instability parameter measuring the competition between quantum-state evolution speed and spectral-gap protection. This quantity provides a local, gauge-invariant, and basis-independent criterion for arbitrary driven Hamiltonians. Near quantum critical points, the instability parameter diverges through inverse gap amplification, recovering the Kibble Zurek freeze-out condition directly from local geometric data. We prove that monotonic occupation-dependent nonlinear regulators geometrically compress the quantum metric, establishing a self-limitation theorem in which nonlinear spectral deformation confines the accessible region of projective Hilbert space under strong driving. The multimode extension yields a matrix-valued instability criterion that identifies collective instability channels invisible to scalar descriptions. The framework naturally extends to open quantum systems through the Bures metric and quantum Fisher geometry, where thermal mixing and Lindblad decay increase the instability threshold through geometric suppression of state distinguishability. The instability threshold further implies a universal geometric lower bound on coherent control time and quantum gate duration. Comments: Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2606.00259 [quant-ph] (or arXiv:2606.00259v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.00259 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexander Tishin M [view email] [v1] Fri, 29 May 2026 18:44:40 UTC (570 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometric Instability and Self-Limitation in Driven Quantum Systems, by A.M.TishinView PDF view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.mes-hall 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?) 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?)