维格纳型矩阵的固态热化假设
László Erdős1, Volodymyr Riabov1
1Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
概括
我们证明了维格纳类型矩阵的Eigenstate热化假设,证明了它在各种随机矩阵组合中的稳定性. 这证实了复杂结构的量子系统中的热化,即使有消失的条目.
科学领域:
- 量子力学就是量子力学.
- 随机矩阵理论是随机矩阵理论.
- 统计物理学的统计物理.
背景情况:
- 固态热化假设 (ETH) 是理解孤立量子系统如何达到热平衡的基石.
- 以前的研究往往侧重于特定的随机矩阵集合或更简单的系统,使得更广泛的适用性不确定.
- 在维格纳型矩阵中研究ETH对于理解复杂量子系统中的热化至关重要.
研究的目的:
- 严格证明Eigenstate热化假设对于一个一般类型的Wigner类型随机矩阵.
- 为了建立在批量频谱内的任意等级的可观测物对波动的最佳控制.
- 在非常一般的条件下证明ETH的稳定性,包括那些具有消失矩阵条目的条件.
主要方法:
- 为维格纳型矩阵的1个和2个分辨率开发和应用等级均最佳局部规律.
- 对具有规律性质的可观察物进行分析.
- 考虑各种变异配置文件,包括那些有很多消失条目.
主要成果:
- 对于光谱质量中的一般维格纳型矩阵,严格证明 Eigenstate热化假设.
- 实现了对任意排名可观测的波动的最佳控制.
- 证明ETH在多种类型的随机矩阵组合中保持稳健.
结论:
- 自体热化假设被证明是维格纳型矩阵的一个强大的现象.
- 这些发现证实了ETH在具有非碎空间结构的量子系统和一般条件下的有效性.
- 这项工作为理解复杂量子系统中的热化提供了重要的理论进步.
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