Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
复制标题
广义斐波那契驱动量子动力学中的完整希尔伯特空间遍历性
DOI：
10.1103/physrevlett.131.250401
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发表时间：
2023
影响因子：
8.6
通讯作者：
Choi, Soonwon
中科院分区：
文献类型：
--
作者：
Pilatowsky-Cameo, Saúl;Dag, Ceren B.;Ho, Wen Wei;Choi, Soonwon
量子动力学的遍历性通常是通过能量本征态的统计性质来定义的，例如单粒子量子混沌中的Berry猜想和多体环境中的本征态热化假设。在这项工作中，我们研究了量子系统是否可以表现出更强的遍历性，其中任何时间演化的态都会随着时间的推移统一访问整个希尔伯特空间。我们称这种现象为完全希尔伯特空间遍历性(CHSE)，它更类似于将遍历性作为一个内在的动力学概念的直观概念。由于(准)能量本征态的存在，CHSE不能适用于与时间无关或甚至是时间周期的哈密顿动力学，这就排除了对整个希尔伯特空间的探索。然而，我们发现存在一类符号复杂度最低的非周期但确定性的驱动器--由斐波那契词及其推广产生--对于这些驱动器，CHSE可以被证明是发生的。我们的结果为理解一般含时量子系统中的热化现象提供了基础。
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 phenomenoncomplete 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.