Rotation numbers for Jacobi matrices with matrix entries
Rotation numbers for Jacobi matrices with matrix entries
复制标题
具有矩阵项的雅可比矩阵的旋转数
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
H. Schulz
中科院分区：
文献类型：
--
作者：
H. Schulz
具有矩阵项的雅可比矩阵是一个在离对角线上有正定块的自伴随块三对角矩阵。给出了其特征值的旋转数计算方法。这是Sturm-Liouville算子离散类似物的振荡定理的一个物质推广。通过实现相应的对称性来处理时间反转不变性的三种普适性类。对于具有随机矩阵项的雅可比矩阵，可以得到状态的积分密度公式，该公式可以通过对误差项进行最优控制的随机性耦合常数进行摄动计算。
A Jacobi matrix with matrix entries is a selfadjoint block tridiagonal matrix with positive definite blocks on the off-diagonals. A rotation number calculation for its eigenvalues is presented. This is a matricial generalization of the oscillation theorem for the discrete analogues of Sturm-Liouville operators. The three universality classes of time reversal invariance are dealt with by implementing the corresponding symmetries. For Jacobi matrices with random matrix entries, this leads to a formula for the integrated density of states which can be calculated perturbatively in the coupling constant of the randomness with an optimal control on the error terms.