Simple slow operators and quantum thermalization

Quantum Physics [Submitted on 14 Apr 2026] Simple slow operators and quantum thermalization Tian-Hua Yang, Sarang Gopalakrishnan, Dmitry A. Abanin We establish a rigorous relation between the thermalization of typical initial states and the dynamics of local operators. We introduce a concept of simple slow operators (SSOs), defined as operators that have a small commutator with the Hamiltonian and have significant small-sized components. We show that if typical initial states (drawn from a low-complexity state ensemble) do not thermalize on timescale t, then SSOs must exist that are approximately conserved up to timescale t. Equivalently, the absence of SSOs implies that typical initial states thermalize. We establish these results by introducing the concept of an ensemble variance norm of an operator, defined as the typical magnitude of the expectation value of that operator with respect to states in the ensemble. For low-entanglement ensembles, the norm is related to operator sizes, allowing us to establish a direct link between operator growth and thermalization. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2604.13172 [quant-ph]   (or arXiv:2604.13172v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.13172 Focus to learn more Submission history From: Tian-Hua Yang [view email] [v1] Tue, 14 Apr 2026 18:00:08 UTC (768 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)