摘要
将复杂网络的邻接矩阵映射为量子系统的哈密顿量,使用随机矩阵理论对该哈密顿量的谱特性进行统计分析。针对谱的最近邻能级间隔分布、数目方差和形状因子等特征量的数值分析表明,当小世界网络模型中重连概率很小时,对应哈密顿量的能谱统计与经典可积量子系统的能谱特性一致;当重连概率大于某一阈值时,其能谱特性与随机矩阵理论中高斯正交系综的能谱特性类似。无标度网络的能谱最近邻能级间隔分布和形状因子也表现出与高斯正交系综能谱类似的特性。研究结果显示出复杂网络的空间拓扑结构转变和量子动力系统的时间演化特性之间具有一定的对应性。
By mapping the adjacency matrix of a complex network to Hamiltonian of a quantum system, the statistical properties of the spectra and eigenstates are analyzed. The spectral statis- tics, i.e. the nearest-neighbor spacing distribution, the number variance and the spectral form factor, are analyzed numerically. The results show that when the rewiring probability of small- world network model is lower, the spectral properties are consistent with those of quantum inte- grable systems. When the rewiring probability is higher than a certain threshold, its energy spec- trum properties are similar to those of the Gaussian orthogonal ensembles in random matrix theo- ry. These results hint that certain analogies may exist between the spatial topology of complex networks and the temporal evolution properties of cluantum dvnamical systems.
出处
《复杂系统与复杂性科学》
EI
CSCD
北大核心
2014年第1期5-11,共7页
Complex Systems and Complexity Science
基金
国家自然科学基金(61104039)
霍英东教育基金会青年教师基金(121066)
国家留学基金
中央高校基本科研业务费专项资金(2012QNB31)
关键词
复杂网络
量子动力系统
谱分析
随机矩阵理论
complex network
quantum dynamical system
spectral analysisl random matrix theory
