Inhomogeneous eigenmode localization, chaos, and correlations in large disordered clusters
Inhomogeneous eigenmode localization, chaos, and correlations in large disordered clusters
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DOI：
10.1103/physreve.56.6494
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发表时间：
1997-12
影响因子：
2.4
通讯作者：
M. Stockman
中科院分区：
文献类型：
--
作者：
M. Stockman
研究了分形团簇和随机非分形团簇的偶极本征模(等离子激子)的统计特性和局域特性。这个问题在数学上等价于同一团簇中具有偶极跳跃幅度的矢量(自旋-1)粒子的量子力学本征问题。在分形团簇中，单个本征模在小尺度上是奇异的，其强度在空间上有强烈的波动。它们既不具有强局域化性质，也不具有弱局域化性质。相反，发生了一种不均匀的局域化模式，其中非常不同相干半径的本征模在相同的频率上共存。在本征值较小的区域，即等离子体激元共振附近，发现了分形团簇本征模的混沌行为。观察到的混沌比正则集上的量子力学问题“更强”，因为本问题的特征是(确定性地)幅度关联函数(动态形状因子)的混沌行为。这种混沌行为包括幅度相关在空间域和频域的相位的快速变化，而其幅度是一个非常平滑的函数。观察到随着本征值的增加，混沌行为和标度行为之间的转变。与分形团簇不同，具有非分形几何结构的随机团簇并不表现出混沌行为，而是随着本征值的减小而呈现出本征模的介观离域相变。
Statistical and localization properties of dipole eigenmodes (plasmons) of fractal and random nonfractal clusters are investigated. The problem is mathematically equivalent to the quantum-mechanical eigenproblem for vector (spin-1) particles with a dipolar hopping amplitude in the same cluster. In fractal clusters, individual eigenmodes are singular on the small scale and their intensity strongly fluctuates in space. They possess neither strong nor weak localization properties. Instead, an inhomogeneous localization pattern takes place, where eigenmodes of very different coherence radii coexist at the same frequency. Chaotic behavior of the eigenmodes is found for fractal clusters in the region of small eigenvalues, i.e., in the vicinity of the plasmon resonance. The observed chaos is ``stronger'' than for quantum-mechanical problems on regular sets in the sense that the present problem is characterized by (deterministically) chaotic behavior of the amplitude correlation function (dynamic form factor). This chaotic behavior consists of rapid changes of the phase of the amplitude correlation in spatial and frequency domains, while its magnitude is a very smooth function. A transition between the chaotic and scaling behavior with increase of eigenvalue is observed. In contrast to fractal clusters, random clusters with nonfractal geometry do not exhibit chaotic behavior, but rather a mesoscopic delocalization transition of the eigenmodes with decrease of eigenvalue.