Formula for The IDS of Periodic Jacobi Matrices
Liangping Qi
TL;DR
This paper establishes a relationship between the integrated density of states (IDS) and the discriminant for periodic Jacobi matrices, using a method based on counting zeros of Bloch wave solutions.
Contribution
It provides a new proof linking the IDS to the discriminant in periodic Jacobi matrices through zero counting of Bloch solutions.
Findings
IDS is related to the discriminant on the spectrum
Method involves counting zeros of Bloch wave solutions
Provides a new perspective on spectral analysis of Jacobi matrices
Abstract
We prove that on the spectrum the integrated density of states (IDS for short) of periodic Jacobi matrices is related to the discriminant. The method is to count the number of generalized zeros of Bloch wave solutions.
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Taxonomy
TopicsOptical and Acousto-Optic Technologies · Quantum optics and atomic interactions · Quantum chaos and dynamical systems