在临界度上,光谱和波函数属性之间的普遍关系
Simon Jiricek1,2, Miroslav Hopjan2,3, Vladimir Kravtsov4
1Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia.
概括
我们在量子关键系统中发现了光谱可压缩性和波函数碎形维度之间的普遍关系. 这一发现表明了混乱量子系统中关键现象的新普遍性类.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 这是量子混沌.
- 无序的系统是无序的系统.
背景情况:
- 量子混沌系统表现出普遍性质,如水平排斥和移位波函数.
- 局部化的波函数导致波桑统计,没有水平排斥.
- 在混乱和局部化之间的边界处的关键系统表现出独特的行为.
研究的目的:
- 在量子混沌本地化关键点调查普遍性.
- 探索光谱可压缩性 (χ) 和波函数碎形维度 (dF) 之间的关系.
- 在不同的对称性和跳跃类型的各种物理系统中测试这种关系.
主要方法:
- 对安德森模型 (3-5维) 和随机带矩阵进行数值分析.
- 研究具有局部和非局部跳跃的系统,有或没有时间逆向对称.
- 在随机带矩阵中测试光谱压缩性的闭式表达式.
主要成果:
- 在研究系统中证实了光谱可压缩性和波函数碎形维度之间的简单,普遍关系.
- 验证了用于光谱可压缩性的衍生闭式表达式的准确性.
- 推导出一种通用函数,将光谱可压缩性与平均水平间距比率 (r) 相关.
结论:
- 关系[公式:参见文本]似乎是广泛的关键模型的通用属性.
- 这些发现表明,在量子临界点有一个新的普遍性类.
- 基于光谱性质的关键系统建立了一个通用函数[公式:见文本].
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