Schulz-Baldes H (2007)
Publication Type: Journal article
Publication year: 2007
Publisher: Angel Jorba & Jaume Timoneda, Eds. & Pubs.
Book Volume: 13
Pages Range: 1-40
URI: http://de.arxiv.org/abs/math-ph/0702050
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.
APA:
Schulz-Baldes, H. (2007). Rotation numbers for Jacobi matrices with matrix entries. Mathematical Physics Electronic Journal, 13, 1-40.
MLA:
Schulz-Baldes, Hermann. "Rotation numbers for Jacobi matrices with matrix entries." Mathematical Physics Electronic Journal 13 (2007): 1-40.
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