Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911775929139200 |
|---|---|
| author | Pilatowsky-Cameo, Saúl Dag, Ceren B. Ho, Wen Wei Choi, Soonwon |
| author_facet | Pilatowsky-Cameo, Saúl Dag, Ceren B. Ho, Wen Wei Choi, Soonwon |
| contents | Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity -- generated by the Fibonacci word and its generalizations -- for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11792 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives Pilatowsky-Cameo, Saúl Dag, Ceren B. Ho, Wen Wei Choi, Soonwon Quantum Physics Statistical Mechanics Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity -- generated by the Fibonacci word and its generalizations -- for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems. |
| title | Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2306.11792 |