由于在一个简单的量子系统中的道化,自值统计中的过渡.
Todd K Timberlake1, Kya Wiggins1
1Department of Physics, Astronomy, and Geology, Berry College, Mount Berry, Georgia 30149-5004, USA.
Physical review. E
|September 19, 2023
概括
这项研究表明,量子能量水平统计数据如何随着模型系统中的传输概率而变化. 固有值统计数据从波桑式转换为高斯式直角集,然后随着传输的增加转换为高斯式.
科学领域:
- 量子力学就是量子力学.
- 统计物理学的统计物理.
- 凝聚物质物理学 凝聚物质物理学
背景情况:
- 量子系统中的能量水平统计与经典动力学有关.
- 常规系统通常显示Poisson统计,而混乱系统则显示随机矩阵统计.
- 系统参数可以驱动正规和混乱的古典动力学之间的过渡,反映在量子自值统计中.
研究的目的:
- 在一个具有变化传输概率的模型系统中调查量子能量固有值统计数据的变化.
- 探索传输概率,自值统计和能量固有状态结构之间的关系.
- 用量子图形来分析系统,并将结果与理论预期进行比较.
主要方法:
- 一个量子系统包括一个无限的正方形以及迪拉克三角洲障碍被建模.
- 通过屏障传输的概率 (T) 系统地变化.
- 分析了能量固有值序列的统计性质,包括水平间距和数值方差.
- 研究了能量固有状态的空间分布.
主要成果:
- 在低传输概率 (T≈0) 的情况下,水平间距分布是Poisson-like.
- 增加T将分布转移到高斯直角集合 (GOE),然后转移到高斯分布,如T→1.
- 数量方差显示了类似的过渡.
- 随着T的增加,能量固有状态从本地化演变为跨井的非本地化.
- 结果与T→0.0的量子图形理论预测一致.
结论:
- 模型系统展示了由传输概率驱动的量子固有值统计中的明确过渡.
- 这种转变反映了基础的古典动态从规律变为混乱的变化.
- 该研究提供了一个可调的量子系统中的统计力学原理的具体例子.
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