临界二维随机矩阵模型中的水平数方差和谱压缩性
Level number variance and spectral compressibility in a critical two-dimensional random matrix model
摘要：
研究了二维随机矩阵模型中矩阵元素按幂律衰减的水平数方差。衰减的幅度由参数b控制。我们分析发现，在小值的b的水平数方差的线性行为，与压缩性chi之间的0和1，这是典型的临界系统。对于大的b值，我们推导出chi=0，正如人们通常在金属相中所期望的那样。使用数值模拟，我们确定的临界值b在这两个阶段之间的过渡发生。
英文摘要：
We study level number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b the level number variance behaves linearly, with the compressibility chi between 0 and 1, which is typical for critical systems. For large values of b, we derive that chi=0, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of b at which the transition between these two phases occurs.
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