Virial expansion for almost diagonal random matrices
Virial expansion for almost diagonal random matrices
复制标题
几乎对角随机矩阵的维里展开
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
V. Kravtsov
中科院分区：
文献类型：
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作者：
O. Yevtushenko;V. Kravtsov
研究了具有高斯独立随机元的Hermitian随机矩阵的能级统计，其中Hi ≥ j是几乎对角随机矩阵的一般系综，|hii| 2~1和|你好，|2 = B（|i − j|）1.我们对谱形因子K（τ）= 1 + bK1（τ）+b2K2（τ）+bK2（τ）的B 1次方进行了正则展开，系数Km（τ）考虑了（m +1）个能级的相互作用.为了计算Km（τ），我们开发了一种图形技术，该技术基于Trotter公式和用（m +1）种颜色着色的图边的组合问题。对于一般函数，找到了K1（τ）和K2（τ）的无穷级数表达式（|i − j|）在高斯正交系综（GOE）、高斯酉系综（GUE）以及它们之间的交叉（几乎酉高斯系综）中。罗森茨韦格-波特和幂律带状矩阵合奏被视为示例。
Energy level statistics of Hermitian random matrices Ĥ with Gaussian independent random entries Hi≥j is studied for a generic ensemble of almost diagonal random matrices with |Hii|2 ~ 1 and |Hi≠j|2 = b(|i − j|) 1. We perform a regular expansion of the spectral form-factor K(τ) = 1 + bK1(τ) + b2K2(τ) + ⋯ in powers of b 1 with the coefficients Km(τ) that take into account interaction of (m + 1) energy levels. To calculate Km(τ), we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges colouring with (m + 1) colours. Expressions for K1(τ) and K2(τ) in terms of infinite series are found for a generic function (|i − j|) in the Gaussian orthogonal ensemble (GOE), the Gaussian unitary ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig–Porter and power-law banded matrix ensembles are considered as examples.