Operator Space Transport and the Emergence of Boundary Time Crystals
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Quantum Physics arXiv:2604.14291 (quant-ph) [Submitted on 15 Apr 2026] Title:Operator Space Transport and the Emergence of Boundary Time Crystals Authors:Dominik Nemeth, Ahsan Nazir, Robert-Jan Slager, Alessandro Principi View a PDF of the paper titled Operator Space Transport and the Emergence of Boundary Time Crystals, by Dominik Nemeth and 3 other authors View PDF HTML (experimental) Abstract:Boundary time crystals (BTCs) are prominent examples of continuous time crystals in collective spin systems governed by Lindbladian evolution. To date, their analysis has mostly relied on semiclassical and numerical approaches. Here, we develop a fully quantum-compatible framework to classify collective spin dynamics and show that BTC behavior emerges from the absence of non-trivial weak symmetries of the Liouvillian. To this end, we introduce an irreducible tensor representation of operator space, in which the Lindbladian dynamics maps onto a non-Hermitian hopping problem. Within this picture, the dynamics corresponds to the transport of operator weight across tensor sectors. This mapping allows an identification of distinct dynamical regimes, including collective precession, pure relaxation, and the BTC phase, within a single unified framework. We show that BTCs arise from non-reciprocal transport in operator space, which delocalizes Liouvillian eigenmodes across multiple tensor sectors. This non-reciprocal transport provides a microscopic mechanism for the insensitivity to initial conditions of BTC oscillations. More broadly, our results establish operator space transport as a perspective for understanding dissipative many-body dynamics and highlights connections to non-Hermitian phenomena. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2604.14291 [quant-ph] (or arXiv:2604.14291v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.14291 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Dominik Nemeth [view email] [v1] Wed, 15 Apr 2026 18:00:04 UTC (409 KB) Full-text links: Access Paper: View a PDF of the paper titled Operator Space Transport and the Emergence of Boundary Time Crystals, by Dominik Nemeth and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)