2025/02/10 by Saúl Pilatowsky-Cameo, Soonwon Choi, Pilatowsky-Cameo, Saúl +3 · 1 citation
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2502.06936
openalex publication_date 2025/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The maximum entropy principle is foundational for statistical analyses of complex dynamics. This principle has been challenged by the findings of a previous work [arXiv:1701.07596], where it was argued that a quantum system driven in time by a certain aperiodic sequence without any explicit symmetries, dubbed the Thue-Morse drive, gives rise to emergent nonergodic steady states which are underpinned by effective conserved quantities. Here, we resolve this apparent tension. We rigorously prove that the Thue-Morse drive achieves a very strong notion of quantum ergodicity in the long-time limit: The time evolution of any initial state uniformly visits every corner of its Hilbert space. On the other hand, we find the dynamics also approximates a Floquet drive for arbitrarily long albeit finite periods of time with no characteristic timescale, resulting in a scale-free ergodic dynamics we call critically slow complete Hilbert-space ergodicity. Furthermore, numerical studies reveal that critically slow complete Hilbert-space ergodicity is not specific to the Thue-Morse drive and is, in fact, exhibited by many other aperiodic drives derived from morphic sequences, i.e., words derived from repeatedly applying substitution rules on basic characters. Our work presents a new class of dynamics in time-dependent quantum systems where full ergodicity is eventually attained, but only after astronomically long times.