Spectral analysis of equilibration: information leakage in isolated quantum systems
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Quantum Physics arXiv:2606.12545 (quant-ph) [Submitted on 10 Jun 2026] Title:Spectral analysis of equilibration: information leakage in isolated quantum systems Authors:André T. Cesário, Marcos G. Alpino, Reinaldo O. Vianna, Tiago Debarba View a PDF of the paper titled Spectral analysis of equilibration: information leakage in isolated quantum systems, by Andr\'e T. Ces\'ario and 3 other authors View PDF HTML (experimental) Abstract:We develop a unified dynamical-spectral framework for equilibration in isolated quantum systems based on a subspace coarse-graining approach. Central to our formulation is the Leakage Fidelity Function (LFF), defined as the probability that a unitarily evolving state escapes the support of its initial subspace. This quantity provides a direct, operational measure of information flow and memory loss without invoking ensemble assumptions or perturbative arguments. We derive universal bounds on temporal fluctuations of the LFF, in terms of the spectral gap structure and the square of the effective dimension, evincing that large spectral delocalization suppresses fluctuations and guarantees equilibration on average. By introducing spectral power distributions and associated entropic measures, we establish a quantitative link between phase mixing, gap participation, and dynamical stability. We further investigate the equilibration timescale by connecting the LFF to quantum speed limits, thereby revealing the average time required for equilibration. Our results provide a state-dependent, geometrically transparent perspective on how spectral complexity and subspace information leakage jointly govern irreversibility in closed quantum many-body systems. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2606.12545 [quant-ph] (or arXiv:2606.12545v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12545 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tiago Debarba [view email] [v1] Wed, 10 Jun 2026 18:00:26 UTC (1,488 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral analysis of equilibration: information leakage in isolated quantum systems, by Andr\'e T. Ces\'ario and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.stat-mech 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?)