Critically Slow Hilbert-Space Ergodicity in Quantum Morphic Drives
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914068750663680 |
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| author | Pilatowsky-Cameo, Saúl Choi, Soonwon Ho, Wen Wei |
| author_facet | Pilatowsky-Cameo, Saúl Choi, Soonwon Ho, Wen Wei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_06936 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critically Slow Hilbert-Space Ergodicity in Quantum Morphic Drives Pilatowsky-Cameo, Saúl Choi, Soonwon Ho, Wen Wei Quantum Physics Statistical Mechanics Chaotic Dynamics 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. |
| title | Critically Slow Hilbert-Space Ergodicity in Quantum Morphic Drives |
| topic | Quantum Physics Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2502.06936 |