Rotation numbers for Jacobi matrices with matrix entries
Mathematical Physics
2016-10-28 v2 math.MP
Abstract
A selfadjoined block tridiagonal matrix with positive definite blocks on the off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer matrix techniques are extended in order to develop a rotation number calculation for its eigenvalues. 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.
Cite
@article{arxiv.math-ph/0702050,
title = {Rotation numbers for Jacobi matrices with matrix entries},
author = {Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:math-ph/0702050},
year = {2016}
}