Dixmier trace and the DOS of magnetic operators
Fabian Belmonte, Giuseppe De Nittis
TL;DR
This paper introduces two new formulas for calculating the trace per unit volume and the integrated density of states of magnetic operators, enabling the use of the Dixmier trace in spectral analysis.
Contribution
It provides novel formulas, including an energy shell formula, for computing spectral invariants of magnetic operators, facilitating approximation and analysis.
Findings
Derived two formulas for trace per unit volume and IDOS
Enabled use of Dixmier trace in spectral analysis of magnetic operators
Proposed an energy shell formula for finite approximation of IDOS
Abstract
The main goal of this work is to provide two new formulas for the computation of the trace per unit volume, and consequently the integrated density of states (IDOS), for magnetic operators. These formulas also permit the use of the Dixmier trace in the spectral analysis of magnetic operators. The second of these formulas, named energy shell formula, permits to approximate the IDOS by a finite sums of averaged expectation values of the spectral projections.
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