Energy-space quantum walks: Thermalization without state convergence
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Quantum Physics arXiv:2605.15339 (quant-ph) [Submitted on 14 May 2026] Title:Energy-space quantum walks: Thermalization without state convergence Authors:Alana Spak dos Santos, Renato Moreira Angelo View a PDF of the paper titled Energy-space quantum walks: Thermalization without state convergence, by Alana Spak dos Santos and Renato Moreira Angelo View PDF HTML (experimental) Abstract:We introduce energy-space quantum walks as a minimal framework to investigate equilibration, thermalization, and irreversibility from an effective-dynamics perspective. By mapping the configuration space of a walk onto a ladder of energy eigenlevels, we reinterpret thermalization as transport in energy space, independently of microscopic system--bath details. At the classical level, the resulting birth--death--lazy dynamics leads to equilibration of the energy distribution and, under suitable conditions, to a Gibbs stationary state. We then embed this dynamics into a unitary, collision-assisted model in which coherence is controlled by a single parameter. A central result is a structural decoupling between population dynamics and coherence generation: while the populations evolve according to the classical process and relax to the Gibbs distribution, the full quantum state exhibits a persistent coherence-induced deviation from the thermal manifold. This establishes a minimal scenario of thermalization without state convergence, where equilibration occurs at the level of populations but not at the level of the full density operator. We quantify this effect using the thermal distance to the Gibbs state and derive perturbative bounds that relate the long-time deviation to classical transport properties. Our results show that coherence acts as a controllable and quantitatively bounded source of nonthermal behavior, providing a clear separation between classical equilibration and genuinely quantum corrections. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.15339 [quant-ph] (or arXiv:2605.15339v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.15339 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alana Spak Dos Santos [view email] [v1] Thu, 14 May 2026 19:06:11 UTC (295 KB) Full-text links: Access Paper: View a PDF of the paper titled Energy-space quantum walks: Thermalization without state convergence, by Alana Spak dos Santos and Renato Moreira AngeloView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)