Rotation numbers for Jacobi matrices with matrix entries

• Autores: Hermann Schulz-Baldes
• Localización: Mathematical Physics Electronic Journal, ISSN-e 1086-6655, Vol. 13, Nº 5, 2007
• Idioma: inglés
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• Resumen

  • 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.