论文标题
真实对称1D随机带矩阵的传输矩阵方法
Transfer matrix approach for the real symmetric 1D random band matrices
论文作者
论文摘要
本文适应了最近开发的超对称传递矩阵方法对1D带矩阵的严格应用与正交对称性的情况。我们考虑$ n \ times n $ block band矩阵由$ w \ times w $ w $ wandom高斯块（由$ j，k \inλ= [1，n] \ cap \ cap \ mathbb {z} $，$ n = nw $）具有固定条目的差异$ j_ {jk} = w^{ - 1}（δ_{j，k}+βδ__{j，k}）$在每个块中。考虑到限制$ w，n \ to \ infty $，我们证明了大部分频谱中此类矩阵的第二个相关函数的行为在大部分频谱中表现出阈值$ w \ sim \ sim \ sqrt {n} $的交叉。
This paper adapts the recently developed rigorous application of the supersymmetric transfer matrix approach for the 1d band matrices to the case of the orthogonal symmetry. We consider $N\times N$ block band matrices consisting of $W\times W$ random Gaussian blocks (parametrized by $j,k \inΛ=[1,n]\cap \mathbb{Z}$, $N=nW$) with a fixed entry's variance $J_{jk}=W^{-1}(δ_{j,k}+βΔ_{j,k})$ in each block. Considering the limit $W, n\to\infty$, we prove that the behavior of the second correlation function of characteristic polynomials of such matrices in the bulk of the spectrum exhibit a crossover near the threshold $W\sim \sqrt{N}$.
