在一般化斐波纳契驱动的量子动力学中,完成希尔伯特空间的厄戈迪性
Saúl Pilatowsky-Cameo1, Ceren B Dag2,3, Wen Wei Ho4,5
1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Physical review letters
|January 5, 2024
概括
量子系统可以通过随着时间的推移探索整个希尔伯特空间来实现完整的希尔伯特空间积分 (CHSE). 这种更强的ergodicity形式可以通过特定的无周期驱动来实现,为量子热化提供了新的见解.
科学领域:
- 量子动力学就是量子动力学.
- 统计力学就是统计力学.
- 混沌理论是一个混乱理论.
背景情况:
- 量子系统中的ergodicity通常由能量固态属性定义,比如贝里推测和固态热化假设.
- 现有的定义将ergodicity限制在统计性质上,而不是对希尔伯特空间的全面探索.
研究的目的:
- 为了研究一种更强的ergodicity形式:完全的希尔伯特空间ergodicity (CHSE).
- 为了确定量子系统是否可以随着时间的推移动态访问希尔伯特空间中的每个状态.
主要方法:
- 在依赖时间的驱动下分析量子动力学.
- 对于特定的驱动器家族,CHSE的数学表述和证明.
- 使用由斐波纳契词和概括生成的确定性驱动器.
主要成果:
- 由于 (准) 能量固有状态,CHSE在时间独立或周期性哈密尔顿式下是不可能的.
- 一个家族的无周期性,确定性的驱动器与最小的复杂性,从斐波那契词派生,使得CHSE.
- 这为量子系统提供了一种机制,使它们能够统一地探索整个希尔伯特空间.
结论:
- 完整的希尔伯特空间 ergodicity (CHSE) 代表了一个新的动态概念在量子系统.
- 周期性驱动,特别是那些基于斐波纳契序列的驱动,是实现CHSE的关键.
- 这些发现促进了对依赖时间的量子力学中的热化理解.
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