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摘要:
For classical billiards, we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As examples of 2D chaotic billiards, we considered the Bunimovich stadium billiard and the Sinai billiard. In the level spacing distribution and spectral rigidity, we found GOE behaviour consistent with predictions from random matrix theory. We studied transport properties and computed a diffusion coefficient. For the Sinai billiard, we found normal diffusion, while the stadium billiard showed anomalous diffusion behaviour. As example of a 2D integrable billiard, we considered the rectangular billiard. We found very rigid behaviour with strongly correlated spectra similar to a Dirac comb. These findings present numerical evidence for universality in level spacing fluctuations to hold in classically integrable systems and in classically fully chaotic systems.
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篇名 Universality in Statistical Measures of Trajectories in Classical Billiard Systems
来源期刊 应用数学(英文) 学科 数学
关键词 CLASSICAL Chaos Dynamical BILLIARDS Random Matrix Theory Level SPACING FLUCTUATIONS UNIVERSALITY
年,卷(期) 2015,(8) 所属期刊栏目
研究方向 页码范围 1407-1425
页数 19页 分类号 O1
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节点文献
CLASSICAL
Chaos
Dynamical
BILLIARDS
Random
Matrix
Theory
Level
SPACING
FLUCTUATIONS
UNIVERSALITY
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研究来源
研究分支
研究去脉
引文网络交叉学科
相关学者/机构
期刊影响力
应用数学(英文)
月刊
2152-7385
武汉市江夏区汤逊湖北路38号光谷总部空间
出版文献量(篇)
1878
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0
总被引数(次)
0
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