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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Marginal intermediate statistics in the excited spectra of the E circle times (b(1) + b(2)) Jahn-Teller system
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Marginal intermediate statistics in the excited spectra of the E circle times (b(1) + b(2)) Jahn-Teller system

机译：E圈时间（b（1）+ b（2））Jahn-Teller系统的激发光谱中的边际中间统计量

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摘要

The long-range spectral density correlations (spectral rigidities (Delta) over bar (3)((n) over bar) and related spectral compressibilities) of the E circle times (b(1) + b(2)) Jahn-Teller model are found strongly nonuniversal with respect to the Hamiltonian parameters and inhomogeneous with respect to the choice of a partial energy segment. However, the partial spectral rigidities exhibit common features: an anomalous linear part for small (n) over bar and a saturation for large (n) over bar. The spectral compressibilities found for the partial spectral segments and averaged over a whole relevant part of the spectrum cumulate close to a well-defined limit pertaining to the semi-Poisson statistics. This is in accordance with similar tendencies revealed in the short-range averaged statistical characteristics of this model investigated in our previous paper (Majernikova and Shpyrko 2006 Phys. Rev. E 73 057202). These features document an inhomogeneous and nonuniversal weakening of level repulsions and nonuniversality of level fluctuations on both long and short energy scales. The nonuniversality and inhomogeneity of the statistical characteristics correspond to a similar behaviour of the chaoticity parameter (a fraction of the chaotic phase space of the trajectories) found for the corresponding semiclassical Hamiltonian. We ascribe the nonuniversal and inhomogeneous nonintegrability behaviour to the changing degree of the brokening of the rotation symmetry when changing parameters of our effectively two-dimensional model. It results in a random distribution of the respective localized wavefunctions at all scales up to the size of an available state space. The multifractal behaviour of the wavefunctions is implied from the analysis of their (averaged) fractal dimensions which range up to 1.5 +/- 0.1 ( for (D) over bar (2)). This might imply the concept of the chaos-assisted tunnelling between the regions of reduced degree of stochasticity through regions of high degree of stochasticity. It supports the analogy with the two-dimensional Anderson model with marginal-asymptotically far metal-insulator transition. The features found allow us to classify the present model as a member of the class with a multifractal eigenfunction statistics characteristic for the spectra with weakened level repulsion similar to the Anderson model close to the metal-insulator transition.
机译：E圈时间（b（1）+ b（2））Jahn-Teller模型的远程光谱密度相关性（条形（3）上的光谱刚度（Delta）（条形上的（n））和相关的光谱可压缩性）相对于哈密顿量参数，我们发现强非普遍性，而对于部分能量段的选择，它们是不均匀的。但是，部分光谱刚度显示出共同的特征：小（n）条以上的线性异常部分，大（n）条以上的饱和线性部分。对于部分光谱段发现的光谱可压缩性，并在整个光谱的整个相关部分取平均值，其累积接近于与半泊松统计有关的明确定义的极限。这与我们先前的论文（Majernikova和Shpyrko 2006 Phys。Rev. E 73 057202）中研究的该模型的短期平均统计特征所揭示的相似趋势一致。这些特征证明了在长和短能量尺度上，液位推斥力的不均匀和非普遍性减弱以及液位波动的不普遍性。统计特性的非通用性和不均匀性对应于为相应的半经典哈密顿量发现的混沌参数的相似行为（轨迹的混沌相空间的一部分）。当改变有效二维模型的参数时，我们将非普遍性和非均匀性的非可积性行为归因于旋转对称性破坏的变化程度。导致各个局部波函数在所有尺度上的随机分布，直至可用状态空间的大小。从对它们的（平均）分形维数的分析中可以隐含出波函数的多重分形行为，分形维数的范围最大为1.5 +/- 0.1（对于（D）在条（2）上）。这可能暗示了在随机性降低的区域之间通过高度随机性的区域之间的混沌辅助隧穿的概念。它支持带有边缘渐近远金属-绝缘体过渡的二维Anderson模型的类比。所发现的特征使我们能够将本模型分类为具有多分形特征函数统计特征的类的成员，该特征具有类似于与金属-绝缘体转变相近的安德森模型的弱水平斥力谱。

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