Energy correlations for a random matrix model of disordered bosons
Energy correlations for a random matrix model of disordered bosons
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DOI：
10.1063/1.2356798
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发表时间：
2006-07
影响因子：
1.3
通讯作者：
T. Lueck;H. Sommers;M. Zirnbauer
中科院分区：
文献类型：
--
作者：
T. Lueck;H. Sommers;M. Zirnbauer
将相互作用量子多体系统的海森堡运动方程线性化，得到了一个位于真实的辛李代数正锥上的时间演化生成元。物理系统中无序的存在决定了在这个圆锥上支持的概率测度。本文分析了一个离散的家庭，这样的指数型措施，并试图捕捉，由一个简单的随机矩阵模型，一些一般的统计特征的无序玻色子准粒子系统的特征频率。所述措施的水平相关函数被证明是那些的行列式过程，和核的过程表示为一个双正交多项式的和。虽然在整体标度极限的相关性是在雅阁与正弦核或高斯酉Entrance普适性，在低频端的频谱的标度行为的一种不寻常的类型被发现。
Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the physical system determines a probability measure with support on this cone. The present paper analyzes a discrete family of such measures of exponential type, and does so in an attempt to capture, by a simple random matrix model, some generic statistical features of the characteristic frequencies of disordered bosonic quasiparticle systems. The level correlation functions of the said measures are shown to be those of a determinantal process, and the kernel of the process is expressed as a sum of biorthogonal polynomials. While the correlations in the bulk scaling limit are in accord with sine-kernel or Gaussian Unitary Ensemble universality, at the low-frequency end of the spectrum an unusual type of scaling behavior is found.