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在轻微扰乱后,对高度退化的哈密尔顿人进行宏观热化
Barbara Roos1, Shoki Sugimoto2,3, Stefan Teufel1
1Mathematics Institute, Eberhard Karls University Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany.
在宏观热平衡 (MATE) 中的系统,如果它们的哈密尔顿式满足自身状态热平衡假设 (ETH),就会热化. 这项研究证明了ETH对于特定的自由费米子系统,并表明MATE一般适用于大多数固有基.
科学领域:
- 量子统计力学就是量子统计力学.
- 凝聚物质理论 凝聚物质理论
- 多体物理学的多体物理学.
背景情况:
- 宏观热平衡 (MATE) 描述了在纯状态下孤立的量子系统.
- 如果哈密尔顿式满足固态热化假设 (ETH),那么热化就会发生,其中每个固态向量都在MATE中.
- 之前的工作证明了ETH对于自由费米子的扰乱哈密尔顿.
研究的目的:
- 为了研究退化量子系统中的热化.
- 为了证明一个特定的自由费米子的非扰动哈密尔顿式的ETH.
- 在具有多个自身基的系统中建立热化的一般条件.
主要方法:
- 免费费米子的非退化的哈密尔顿式的ETH的数学证明.
- 分析一个MATE固有基础的存在与MATE在其他固有基础中的流行之间的关系.
- 证明一个小的通用扰动通常会导致ETH满足和热化.
主要成果:
- 已经证明ETH对N自由费米子的非扰动哈密尔顿式持有,这意味着所有初始状态都会变热.
- 在MATE中存在单个自身基础的存在通常意味着大多数自身基础也在MATE中.
- 哈密尔顿式的通用扰动导致ETH满足和所有状态的普遍热化.
结论:
- 退化的哈密尔顿人可以表现出热化,如果ETH持有所有自身基础.
- 该研究为了解量子系统中的热化提供了一个一般的框架,将MATE属性与不同的固有基础联系起来.
- 这些发现证实,通用扰动确保了量子多体系统中的ETH和热化.
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