临界随机矩阵系综中的返回概率和标度指数
Return probability and scaling exponents in the critical random matrix ensemble
摘要：
研究了强多重分形体系中临界随机矩阵系综返回概率的渐近行为。期望返回概率在大时间或大系统规模的限制下显示临界标度。利用超对称维里展开，我们确定了标度律，并得到了波函数$d_2$的分维和动力学标度指数$μ$的解析表达式.通过比较，我们验证了Chalker模型对动力学标度的有效性。
英文摘要：
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large system size. Using the supersymmetric virial expansion we confirm the scaling law and find analytical expressions for the fractal dimension of the wave functions $d_2$ and the dynamical scaling exponent $μ$. By comparing them we verify the validity of the Chalker's ansatz for dynamical scaling.
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